diff --git a/.circleci/prepare.sh b/.circleci/prepare.sh
index 083c6d19..dfd3aeef 100644
--- a/.circleci/prepare.sh
+++ b/.circleci/prepare.sh
@@ -1,6 +1,6 @@
 $PYTHON --version
 $PYTHON -m pip --version
-$PYTHON -m pip install -q --user --ignore-installed --upgrade "virtualenv<20"
+$PYTHON -m pip install -q --user --ignore-installed --upgrade virtualenv
 $PYTHON -m virtualenv -p $PYTHON venv
 venv/bin/python -m pip install -r requirements-dev.txt
 venv/bin/python -m pip freeze
diff --git a/.travis.yml b/.travis.yml
index d5215b04..46de3bac 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -9,6 +9,30 @@ matrix:
       services: docker
       env: PYTHON=python
 
+    # Linux Python 3
+    - sudo: required
+      language: python
+      python: 3.5
+      services: docker
+      arch: arm64
+      env: PYTHON=python
+
+    # Linux Python 3
+    - sudo: required
+      language: python
+      python: 3.5
+      services: docker
+      arch: ppc64le
+      env: PYTHON=python
+
+    # Linux Python 3
+    - sudo: required
+      language: python
+      python: 3.5
+      services: docker
+      arch: s390x
+      env: PYTHON=python
+
     # macOS Python 3
     - os: osx
       env: PYTHON=python3
diff --git a/CI.md b/CI.md
index 3b43a2e6..d01ca50c 100644
--- a/CI.md
+++ b/CI.md
@@ -7,3 +7,5 @@ This is a summary of the Python versions and platforms covered by the different
 | Windows  | TravisCI         | Azure Pipelines  | AppVeyor              | Azure Pipelines  |
 
 > ¹ Python version not really pinned, but dependent on the (default) version of image used.
+
+Non-x86 architectures are covered on Travis CI using Python 3.5.
diff --git a/README.md b/README.md
index 2989eac2..d918c808 100644
--- a/README.md
+++ b/README.md
@@ -15,17 +15,19 @@ Python wheels are great. Building them across **Mac, Linux, Windows**, on **mult
 What does it do?
 ----------------
 
-|   | macOS 10.9+ x86_64 | manylinux i686 | manylinux x86_64 |  Windows 32bit | Windows 64bit |
-|---|---|---|---|---|---|
-| Python 2.7 | ✅ | ✅ | ✅ | ✅¹ | ✅¹ |
-| Python 3.5 | ✅ | ✅ | ✅ | ✅  | ✅  |
-| Python 3.6 | ✅ | ✅ | ✅ | ✅  | ✅  |
-| Python 3.7 | ✅ | ✅ | ✅ | ✅  | ✅  |
-| Python 3.8 | ✅ | ✅ | ✅ | ✅  | ✅  |
+|   | macOS x86_64 | Windows 64bit | Windows 32bit | manylinux x86_64 | manylinux i686 | manylinux aarch64 | manylinux ppc64le | manylinux s390x |
+|---|---|---|---|---|---|---|---|---|
+| CPython 2.7     | ✅ | ✅¹ | ✅¹ | ✅ | ✅ |     |     |     |
+| CPython 3.5     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅  | ✅  | ✅  |
+| CPython 3.6     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅  | ✅  | ✅  |
+| CPython 3.7     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅  | ✅  | ✅  |
+| CPython 3.8     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅  | ✅  | ✅  |
+| PyPy 2.7 v7.3.0 | ✅ |     | ✅  | ✅ |    |     |     |     |
+| PyPy 3.6 v7.3.0 | ✅ |     | ✅  | ✅ |    |     |     |     |
 
-> ¹ Not supported on Travis
+<sup>¹ Not supported on Travis</sup>
 
-- Builds manylinux, macOS and Windows (32 and 64bit) wheels using Azure Pipelines, Travis CI, AppVeyor, and CircleCI
+- Builds manylinux, macOS and Windows wheels for CPython and PyPy using Azure Pipelines, Travis CI, AppVeyor, and CircleCI
 - Bundles shared library dependencies on Linux and macOS through [auditwheel](https://github.com/pypa/auditwheel) and [delocate](https://github.com/matthew-brett/delocate)
 - Runs the library test suite against the wheel-installed version of your library
 
@@ -48,7 +50,7 @@ Usage
 Example setup
 -------------
 
-To build manylinux, macOS, and Windows  wheels on Travis CI and upload them to PyPI whenever you tag a version, you could use this `.travis.yml`:
+To build manylinux, macOS, and Windows wheels on Travis CI and upload them to PyPI whenever you tag a version, you could use this `.travis.yml`:
 
 ```yaml
 language: python
@@ -73,15 +75,19 @@ env:
     # Note: TWINE_PASSWORD is set to a PyPI API token in Travis settings
 
 install:
-  - python -m pip install twine cibuildwheel==1.1.0
+  - python3 -m pip install cibuildwheel==1.1.0
 
 script:
   # build the wheels, put them into './wheelhouse'
-  - python -m cibuildwheel --output-dir wheelhouse
+  - python3 -m cibuildwheel --output-dir wheelhouse
 
 after_success:
   # if the release was tagged, upload them to PyPI
-  - if [[ $TRAVIS_TAG ]]; then python -m twine upload wheelhouse/*.whl; fi
+  - |
+    if [[ $TRAVIS_TAG ]]; then
+      python3 -m pip install twine
+      python3 -m twine upload wheelhouse/*.whl
+    fi
 ```
 
 For more information, including how to build on Appveyor, Azure, CircleCI, check out the [documentation](https://cibuildwheel.readthedocs.org) and also check out [the examples](https://github.com/joerick/cibuildwheel/tree/master/examples).
@@ -96,7 +102,7 @@ Options
 | **Build environment** | [`CIBW_ENVIRONMENT`](https://cibuildwheel.readthedocs.io/en/stable/options/#environment)  | Set environment variables needed during the build |
 |   | [`CIBW_BEFORE_BUILD`](https://cibuildwheel.readthedocs.io/en/stable/options/#before-build)  | Execute a shell command preparing each wheel's build |
 |   | [`CIBW_REPAIR_WHEEL_COMMAND`](https://cibuildwheel.readthedocs.io/en/stable/options/#repair-wheel-command)  | Execute a shell command to repair each (non-pure Python) built wheel |
-|   | [`CIBW_MANYLINUX_X86_64_IMAGE`](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)  [`CIBW_MANYLINUX_I686_IMAGE`](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)  | Specify alternative manylinux docker images |
+|   | [`CIBW_MANYLINUX_X86_64_IMAGE`](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)  [`CIBW_MANYLINUX_I686_IMAGE`](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)  [`CIBW_MANYLINUX_PYPY_X86_64_IMAGE`](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)  | Specify alternative manylinux docker images |
 | **Testing** | [`CIBW_TEST_COMMAND`](https://cibuildwheel.readthedocs.io/en/stable/options/#test-command)  | Execute a shell command to test each built wheel |
 |   | [`CIBW_TEST_REQUIRES`](https://cibuildwheel.readthedocs.io/en/stable/options/#test-requires)  | Install Python dependencies before running the tests |
 |   | [`CIBW_TEST_EXTRAS`](https://cibuildwheel.readthedocs.io/en/stable/options/#test-extras)  | Install your wheel for testing using extras_require |
@@ -136,8 +142,8 @@ Changelog
 
 _7 December 2019_
 
-- ✨ Add support for building manylinux2014 wheels. To use, set 
-  `CIBW_MANYLINUX_X86_64_IMAGE` and CIBW_MANYLINUX_I686_IMAGE to 
+- ✨ Add support for building manylinux2014 wheels. To use, set
+  `CIBW_MANYLINUX_X86_64_IMAGE` and CIBW_MANYLINUX_I686_IMAGE to
   `manylinux2014`.
 - ✨ Add support for [Linux on Appveyor](https://www.appveyor.com/blog/2018/03/06/appveyor-for-linux/) (#204, #207)
 - ✨ Add `CIBW_REPAIR_WHEEL_COMMAND` env variable, for changing how
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
index 74d78395..4b5aabd3 100644
--- a/azure-pipelines.yml
+++ b/azure-pipelines.yml
@@ -10,7 +10,7 @@ jobs:
         python ./bin/run_tests.py
 
 - job: macos_35
-  pool: {vmImage: 'macOS-10.13'}
+  pool: {vmImage: 'macOS-10.15'}
   steps:
     - task: UsePythonVersion@0
       inputs:
@@ -20,7 +20,7 @@ jobs:
         python ./bin/run_tests.py
 
 - job: macos_38
-  pool: {vmImage: 'macOS-10.13'}
+  pool: {vmImage: 'macOS-10.15'}
   steps:
     - task: UsePythonVersion@0
       inputs:
diff --git a/cibuildwheel/__main__.py b/cibuildwheel/__main__.py
index 63527f22..13fcc881 100644
--- a/cibuildwheel/__main__.py
+++ b/cibuildwheel/__main__.py
@@ -170,6 +170,10 @@ def main():
     if platform == 'linux':
         manylinux_x86_64_image = os.environ.get('CIBW_MANYLINUX_X86_64_IMAGE', 'manylinux2010')
         manylinux_i686_image = os.environ.get('CIBW_MANYLINUX_I686_IMAGE', 'manylinux2010')
+        manylinux_pypy_x86_64_image = os.environ.get('CIBW_MANYLINUX_PYPY_X86_64_IMAGE', 'manylinux2010')
+        manylinux_aarch64_image = os.environ.get('CIBW_MANYLINUX_AARCH64_IMAGE', 'manylinux2014')
+        manylinux_ppc64le_image = os.environ.get('CIBW_MANYLINUX_PPC64LE_IMAGE', 'manylinux2014')
+        manylinux_s390x_image = os.environ.get('CIBW_MANYLINUX_S390X_IMAGE', 'manylinux2014')
 
         pinned_docker_images_file = os.path.join(
             os.path.dirname(__file__), 'resources', 'pinned_docker_images.cfg'
@@ -194,6 +198,28 @@ def main():
         else:
             manylinux_images['i686'] = manylinux_i686_image
 
+        if manylinux_pypy_x86_64_image in pinned_docker_images:
+            manylinux_images['pypy_x86_64'] = pinned_docker_images[manylinux_pypy_x86_64_image]['pypy_x86_64']
+        else:
+            manylinux_images['pypy_x86_64'] = manylinux_pypy_x86_64_image
+
+        if manylinux_aarch64_image in pinned_docker_images:
+            manylinux_images['aarch64'] = pinned_docker_images[manylinux_aarch64_image]['aarch64']
+        else:
+            manylinux_images['aarch64'] = manylinux_aarch64_image
+
+        if manylinux_ppc64le_image in pinned_docker_images:
+            manylinux_images['ppc64le'] = pinned_docker_images[manylinux_ppc64le_image]['ppc64le']
+        else:
+            manylinux_images['ppc64le'] = manylinux_ppc64le_image
+
+        if manylinux_s390x_image in pinned_docker_images:
+            manylinux_images['x390x'] = pinned_docker_images[manylinux_s390x_image]['x390x']
+        else:
+            manylinux_images['x390x'] = manylinux_s390x_image
+
+        manylinux_images['pypy_x86_64'] = ''
+
         build_options.update(
             manylinux_images=manylinux_images
         )
diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index e31e00ca..87251d8f 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -1,4 +1,5 @@
 import os
+import platform
 import shlex
 import subprocess
 import sys
@@ -12,25 +13,59 @@ from .util import (
 )
 
 
+def matches_platform(identifier):
+    pm = platform.machine()
+    if pm == "x86_64":
+        # x86_64 machines can run i686 docker containers
+        if identifier.endswith('x86_64') or identifier.endswith('i686'):
+            return True
+    elif pm == "i686":
+        if identifier.endswith('i686'):
+            return True
+    elif pm == "aarch64":
+        if identifier.endswith('aarch64'):
+            return True
+    elif pm == "ppc64le":
+        if identifier.endswith('ppc64le'):
+            return True
+    elif pm == "s390x":
+        if identifier.endswith('s390x'):
+            return True
+    return False
+
+
 def get_python_configurations(build_selector):
     PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'identifier', 'path'])
     python_configurations = [
-        PythonConfiguration(version='2.7', identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27m'),
-        PythonConfiguration(version='2.7', identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27mu'),
-        PythonConfiguration(version='3.5', identifier='cp35-manylinux_x86_64', path='/opt/python/cp35-cp35m'),
-        PythonConfiguration(version='3.6', identifier='cp36-manylinux_x86_64', path='/opt/python/cp36-cp36m'),
-        PythonConfiguration(version='3.7', identifier='cp37-manylinux_x86_64', path='/opt/python/cp37-cp37m'),
-        PythonConfiguration(version='3.8', identifier='cp38-manylinux_x86_64', path='/opt/python/cp38-cp38'),
-        PythonConfiguration(version='2.7', identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27m'),
-        PythonConfiguration(version='2.7', identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27mu'),
-        PythonConfiguration(version='3.5', identifier='cp35-manylinux_i686', path='/opt/python/cp35-cp35m'),
-        PythonConfiguration(version='3.6', identifier='cp36-manylinux_i686', path='/opt/python/cp36-cp36m'),
-        PythonConfiguration(version='3.7', identifier='cp37-manylinux_i686', path='/opt/python/cp37-cp37m'),
-        PythonConfiguration(version='3.8', identifier='cp38-manylinux_i686', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27m'),
+        PythonConfiguration(identifier='cp27-manylinux_x86_64', path='/opt/python/cp27-cp27mu'),
+        PythonConfiguration(identifier='cp35-manylinux_x86_64', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(identifier='cp36-manylinux_x86_64', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(identifier='cp37-manylinux_x86_64', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(identifier='cp38-manylinux_x86_64', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27m'),
+        PythonConfiguration(identifier='cp27-manylinux_i686', path='/opt/python/cp27-cp27mu'),
+        PythonConfiguration(identifier='cp35-manylinux_i686', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(identifier='cp36-manylinux_i686', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(identifier='cp37-manylinux_i686', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(identifier='cp38-manylinux_i686', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(identifier='pp27-manylinux_x86_64', path='/opt/python/pp27-pypy_73'),
+        PythonConfiguration(identifier='pp36-manylinux_x86_64', path='/opt/python/pp36-pypy36_pp73'),
+        PythonConfiguration(identifier='cp35-manylinux_aarch64', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(identifier='cp36-manylinux_aarch64', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(identifier='cp37-manylinux_aarch64', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(identifier='cp38-manylinux_aarch64', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(identifier='cp35-manylinux_ppc64le', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(identifier='cp36-manylinux_ppc64le', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(identifier='cp37-manylinux_ppc64le', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(identifier='cp38-manylinux_ppc64le', path='/opt/python/cp38-cp38'),
+        PythonConfiguration(identifier='cp35-manylinux_s390x', path='/opt/python/cp35-cp35m'),
+        PythonConfiguration(identifier='cp36-manylinux_s390x', path='/opt/python/cp36-cp36m'),
+        PythonConfiguration(identifier='cp37-manylinux_s390x', path='/opt/python/cp37-cp37m'),
+        PythonConfiguration(identifier='cp38-manylinux_s390x', path='/opt/python/cp38-cp38'),
     ]
-
     # skip builds as required
-    return [c for c in python_configurations if build_selector(c.identifier)]
+    return [c for c in python_configurations if matches_platform(c.identifier) and build_selector(c.identifier)]
 
 
 def build(project_dir, output_dir, test_command, test_requires, test_extras, before_build, build_verbosity, build_selector, repair_command, environment, manylinux_images, dependency_constraints):
@@ -45,12 +80,16 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
 
     python_configurations = get_python_configurations(build_selector)
     platforms = [
-        ('manylinux_x86_64', manylinux_images['x86_64']),
-        ('manylinux_i686', manylinux_images['i686']),
+        ('cp', 'manylinux_x86_64', manylinux_images['x86_64']),
+        ('cp', 'manylinux_i686', manylinux_images['i686']),
+        ('cp', 'manylinux_aarch64', manylinux_images['aarch64']),
+        ('cp', 'manylinux_ppc64le', manylinux_images['ppc64le']),
+        ('cp', 'manylinux_s390x', manylinux_images['s390x']),
+        ('pp', 'manylinux_x86_64', manylinux_images['pypy_x86_64']),
     ]
 
-    for platform_tag, docker_image in platforms:
-        platform_configs = [c for c in python_configurations if c.identifier.endswith(platform_tag)]
+    for implementation, platform_tag, docker_image in platforms:
+        platform_configs = [c for c in python_configurations if c.identifier.startswith(implementation) and c.identifier.endswith(platform_tag)]
         if not platform_configs:
             continue
 
@@ -84,14 +123,19 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
                         cd /project
 
                         PYBIN="{config_python_bin}"
-                        export PATH="$PYBIN:$PATH"
 
+                        export PATH="$PYBIN:$PATH"
                         {environment_exports}
 
                         # check the active python and pip are in PYBIN
-                        # if `test` returns false, the script will exit due to errexit
-                        test "$(which pip)" = "$PYBIN/pip"
-                        test "$(which python)" = "$PYBIN/python"
+                        if [ "$(which pip)" != "$PYBIN/pip" ]; then
+                        echo "cibuildwheel: python available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert python above it."
+                        exit 1
+                        fi
+                        if [ "$(which python)" != "$PYBIN/python" ]; then
+                        echo "cibuildwheel: pip available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert pip above it."
+                        exit 1
+                        fi
 
                         if [ ! -z {before_build} ]; then
                             sh -c {before_build}
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 40c8e8c3..40db5250 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -2,6 +2,7 @@ import os
 import shlex
 import shutil
 import subprocess
+import sys
 import tempfile
 from collections import namedtuple
 from glob import glob
@@ -14,6 +15,16 @@ from .util import (
 )
 
 
+def call(args, env=None, cwd=None, shell=False):
+    # print the command executing for the logs
+    if shell:
+        print('+ %s' % args)
+    else:
+        print('+ ' + ' '.join(shlex.quote(a) for a in args))
+
+    return subprocess.check_call(args, env=env, cwd=cwd, shell=shell)
+
+
 def get_python_configurations(build_selector):
     PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'identifier', 'url'])
     python_configurations = [
@@ -22,12 +33,79 @@ def get_python_configurations(build_selector):
         PythonConfiguration(version='3.6', identifier='cp36-macosx_x86_64', url='https://www.python.org/ftp/python/3.6.8/python-3.6.8-macosx10.9.pkg'),
         PythonConfiguration(version='3.7', identifier='cp37-macosx_x86_64', url='https://www.python.org/ftp/python/3.7.6/python-3.7.6-macosx10.9.pkg'),
         PythonConfiguration(version='3.8', identifier='cp38-macosx_x86_64', url='https://www.python.org/ftp/python/3.8.1/python-3.8.1-macosx10.9.pkg'),
+        PythonConfiguration(version='2.7-v7.3.0', identifier='pp27-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-osx64.tar.bz2'),
+        PythonConfiguration(version='3.6-v7.3.0', identifier='pp36-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-osx64.tar.bz2'),
     ]
 
     # skip builds as required
     return [c for c in python_configurations if build_selector(c.identifier)]
 
 
+SYMLINKS_DIR = '/tmp/cibw_bin'
+
+
+def make_symlinks(installation_bin_path, python_executable, pip_executable):
+    assert os.path.exists(os.path.join(installation_bin_path, python_executable))
+
+    # Python bin folders on Mac don't symlink `python3` to `python`, and neither
+    # does PyPy for `pypy` or `pypy3`, so we do that so `python` and `pip` always
+    # point to the active configuration.
+    if os.path.exists(SYMLINKS_DIR):
+        shutil.rmtree(SYMLINKS_DIR)
+    os.makedirs(SYMLINKS_DIR)
+
+    os.symlink(os.path.join(installation_bin_path, python_executable), os.path.join(SYMLINKS_DIR, 'python'))
+    os.symlink(os.path.join(installation_bin_path, python_executable + '-config'), os.path.join(SYMLINKS_DIR, 'python-config'))
+    os.symlink(os.path.join(installation_bin_path, pip_executable), os.path.join(SYMLINKS_DIR, 'pip'))
+
+
+def install_cpython(version, url):
+    installed_system_packages = subprocess.check_output(['pkgutil', '--pkgs'], universal_newlines=True).splitlines()
+
+    # if this version of python isn't installed, get it from python.org and install
+    python_package_identifier = 'org.python.Python.PythonFramework-{}'.format(version)
+    if python_package_identifier not in installed_system_packages:
+        # download the pkg
+        download(url, '/tmp/Python.pkg')
+        # install
+        call(['sudo', 'installer', '-pkg', '/tmp/Python.pkg', '-target', '/'])
+        # patch open ssl
+        if version == '3.5':
+            open_ssl_patch_url = 'https://github.com/mayeut/patch-macos-python-openssl/releases/download/v1.0.2t/patch-macos-python-%s-openssl-v1.0.2t.tar.gz' % version
+            download(open_ssl_patch_url, '/tmp/python-patch.tar.gz')
+            call(['sudo', 'tar', '-C', '/Library/Frameworks/Python.framework/Versions/{}/'.format(version), '-xmf', '/tmp/python-patch.tar.gz'])
+
+    installation_bin_path = '/Library/Frameworks/Python.framework/Versions/{}/bin'.format(version)
+    python_executable = 'python3' if version[0] == '3' else 'python'
+    pip_executable = 'pip3' if version[0] == '3' else 'pip'
+    make_symlinks(installation_bin_path, python_executable, pip_executable)
+
+    return installation_bin_path
+
+
+def install_pypy(version, url):
+    pypy_tar_bz2 = url.rsplit('/', 1)[-1]
+    assert pypy_tar_bz2.endswith(".tar.bz2")
+    pypy_base_filename = os.path.splitext(os.path.splitext(pypy_tar_bz2)[0])[0]
+    installation_path = os.path.join('/tmp', pypy_base_filename)
+    if not os.path.exists(installation_path):
+        download(url, os.path.join("/tmp", pypy_tar_bz2))
+        call(['tar', '-C', '/tmp', '-xf', os.path.join("/tmp", pypy_tar_bz2)])
+
+        # fix PyPy 7.3.0 bug resulting in wrong macOS platform tag
+        if version.endswith("-v7.3.0") and version[0] == '3':
+            patch_file = os.path.abspath(os.path.join(os.path.dirname(__file__), 'resources', 'pypy3.6.patch'))
+            sysconfigdata_file = os.path.join(installation_path, 'lib_pypy', '_sysconfigdata.py')
+            call(['patch', sysconfigdata_file, patch_file, '-N'])  # Always has nonzero return code
+
+    installation_bin_path = os.path.join(installation_path, 'bin')
+    python_executable = 'pypy3' if version[0] == '3' else 'pypy'
+    pip_executable = 'pip3' if version[0] == '3' else 'pip'
+    make_symlinks(installation_bin_path, python_executable, pip_executable)
+
+    return installation_bin_path
+
+
 def build(project_dir, output_dir, test_command, test_requires, test_extras, before_build, build_verbosity, build_selector, repair_command, environment, dependency_constraints):
     abs_project_dir = os.path.abspath(project_dir)
     temp_dir = tempfile.mkdtemp(prefix='cibuildwheel')
@@ -36,57 +114,37 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
 
     python_configurations = get_python_configurations(build_selector)
 
-    pkgs_output = subprocess.check_output(['pkgutil', '--pkgs'], universal_newlines=True)
-    installed_system_packages = pkgs_output.splitlines()
-
-    def call(args, env=None, cwd=None, shell=False):
-        # print the command executing for the logs
-        if shell:
-            print('+ %s' % args)
-        else:
-            print('+ ' + ' '.join(shlex.quote(a) for a in args))
-
-        return subprocess.check_call(args, env=env, cwd=cwd, shell=shell)
-
     for config in python_configurations:
-        # if this version of python isn't installed, get it from python.org and install
-        python_package_identifier = 'org.python.Python.PythonFramework-%s' % config.version
-        if python_package_identifier not in installed_system_packages:
-            # download the pkg
-            download(config.url, '/tmp/Python.pkg')
-            # install
-            call(['sudo', 'installer', '-pkg', '/tmp/Python.pkg', '-target', '/'])
-            # patch open ssl
-            if config.version == '3.5':
-                open_ssl_patch_url = 'https://github.com/mayeut/patch-macos-python-openssl/releases/download/v1.0.2t/patch-macos-python-%s-openssl-v1.0.2t.tar.gz' % config.version
-                download(open_ssl_patch_url, '/tmp/python-patch.tar.gz')
-                call(['sudo', 'tar', '-C', '/Library/Frameworks/Python.framework/Versions/%s/' % config.version, '-xmf', '/tmp/python-patch.tar.gz'])
-
-        installation_bin_path = '/Library/Frameworks/Python.framework/Versions/{}/bin'.format(config.version)
-        assert os.path.exists(os.path.join(installation_bin_path, 'python3' if config.version[0] == '3' else 'python'))
-
-        # Python bin folders on Mac don't symlink python3 to python, so we do that
-        # so `python` and `pip` always point to the active configuration.
-        if os.path.exists('/tmp/cibw_bin'):
-            shutil.rmtree('/tmp/cibw_bin')
-        os.makedirs('/tmp/cibw_bin')
-
-        if config.version[0] == '3':
-            os.symlink(os.path.join(installation_bin_path, 'python3'), '/tmp/cibw_bin/python')
-            os.symlink(os.path.join(installation_bin_path, 'python3-config'), '/tmp/cibw_bin/python-config')
-            os.symlink(os.path.join(installation_bin_path, 'pip3'), '/tmp/cibw_bin/pip')
+        if config.identifier.startswith('cp'):
+            installation_bin_path = install_cpython(config.version, config.url)
+        elif config.identifier.startswith('pp'):
+            installation_bin_path = install_pypy(config.version, config.url)
+        else:
+            raise ValueError("Unknown Python implementation")
 
         env = os.environ.copy()
         env['PATH'] = os.pathsep.join([
-            '/tmp/cibw_bin',
+            SYMLINKS_DIR,
             installation_bin_path,
             env['PATH'],
         ])
+
+        # Fix issue with site.py setting the wrong `sys.prefix`, `sys.exec_prefix`,
+        # `sys.path`, ... for PyPy: https://foss.heptapod.net/pypy/pypy/issues/3175
+        # Also fix an issue with the shebang of installed scripts inside the
+        # testing virtualenv- see https://github.com/theacodes/nox/issues/44 and
+        # https://github.com/pypa/virtualenv/issues/620
+        # Also see https://github.com/python/cpython/pull/9516
+        env.pop('__PYVENV_LAUNCHER__', None)
         env = environment.as_dictionary(prev_environment=env)
 
         # check what version we're on
         call(['which', 'python'], env=env)
         call(['python', '--version'], env=env)
+        which_python = subprocess.check_output(['which', 'python'], env=env, universal_newlines=True).strip()
+        if which_python != '/tmp/cibw_bin/python':
+            print("cibuildwheel: python available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert python above it.", file=sys.stderr)
+            exit(1)
 
         dependency_constraint_flags = []
         if dependency_constraints:
@@ -95,9 +153,14 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
             ]
 
         # install pip & wheel
-        call(['python', get_pip_script, '--no-setuptools', '--no-wheel'] + dependency_constraint_flags, env=env, cwd="/tmp")
+        call(['python', get_pip_script] + dependency_constraint_flags, env=env, cwd="/tmp")
         assert os.path.exists(os.path.join(installation_bin_path, 'pip'))
+        call(['which', 'pip'], env=env)
         call(['pip', '--version'], env=env)
+        which_pip = subprocess.check_output(['which', 'pip'], env=env, universal_newlines=True).strip()
+        if which_pip != '/tmp/cibw_bin/pip':
+            print("cibuildwheel: pip available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert pip above it.", file=sys.stderr)
+            exit(1)
         call(['pip', 'install', '--upgrade', 'setuptools', 'wheel', 'delocate'] + dependency_constraint_flags, env=env)
 
         # setup target platform, only required for python 3.5
@@ -150,9 +213,6 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
                 os.path.join(venv_dir, 'bin'),
                 virtualenv_env['PATH'],
             ])
-            # Fix some weird issue with the shebang of installed scripts
-            # See https://github.com/theacodes/nox/issues/44 and https://github.com/pypa/virtualenv/issues/620
-            virtualenv_env.pop('__PYVENV_LAUNCHER__', None)
 
             # check that we are using the Python from the virtual environment
             call(['which', 'python'], env=virtualenv_env)
diff --git a/cibuildwheel/resources/pypy3.6.patch b/cibuildwheel/resources/pypy3.6.patch
new file mode 100644
index 00000000..b42d4bfd
--- /dev/null
+++ b/cibuildwheel/resources/pypy3.6.patch
@@ -0,0 +1,7 @@
+--- a/lib_pypy/_sysconfigdata.py	Tue Jan 28 22:54:59 2020 +0200
++++ b/lib_pypy/_sysconfigdata.py	Wed Jan 29 19:21:23 2020 +0200
+@@ -47,4 +47,5 @@
+     build_time_vars['CC'] += ' -arch %s' % (arch,)
+     if "CXX" in build_time_vars:
+         build_time_vars['CXX'] += ' -arch %s' % (arch,)
++    build_time_vars['MACOSX_DEPLOYMENT_TARGET'] = '10.7'
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index ab15db37..a7c38fbc 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -1,9 +1,11 @@
 import os
 import shutil
 import subprocess
+import sys
 import tempfile
 from collections import namedtuple
 from glob import glob
+from zipfile import ZipFile
 
 from .util import (
     download,
@@ -17,37 +19,54 @@ IS_RUNNING_ON_AZURE = os.path.exists('C:\\hostedtoolcache')
 IS_RUNNING_ON_TRAVIS = os.environ.get('TRAVIS_OS_NAME') == 'windows'
 
 
-def get_python_path(config):
-    nuget_args = get_nuget_args(config)
-    return os.path.join(nuget_args[-1], nuget_args[0] + "." + config.version, "tools")
+def simple_shell(args, env=None, cwd=None):
+    print('+ ' + ' '.join(args))
+    args = ['cmd', '/E:ON', '/V:ON', '/C'] + args
+    return subprocess.check_call(' '.join(args), env=env, cwd=cwd)
 
 
-def get_nuget_args(configuration):
-    python_name = "python" if configuration.version[0] == '3' else "python2"
-    if configuration.arch == "32":
-        python_name = python_name + "x86"
-    return [python_name, "-Version", configuration.version, "-OutputDirectory", "C:/cibw/python"]
+if IS_RUNNING_ON_AZURE or IS_RUNNING_ON_TRAVIS:
+    shell = simple_shell
+else:
+    run_with_env = os.path.abspath(os.path.join(os.path.dirname(__file__), 'resources', 'appveyor_run_with_env.cmd'))
+
+    # run_with_env is a cmd file that sets the right environment variables
+    # to build on AppVeyor.
+    def shell(args, env=None, cwd=None):
+        # print the command executing for the logs
+        print('+ ' + ' '.join(args))
+        args = ['cmd', '/E:ON', '/V:ON', '/C', run_with_env] + args
+        return subprocess.check_call(' '.join(args), env=env, cwd=cwd)
+
+
+def get_nuget_args(version, arch):
+    python_name = 'python' if version[0] == '3' else 'python2'
+    if arch == '32':
+        python_name = python_name + 'x86'
+    return [python_name, '-Version', version, '-OutputDirectory', 'C:\\cibw\\python']
 
 
 def get_python_configurations(build_selector):
-    PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'arch', 'identifier'])
+    PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'arch', 'identifier', 'url'])
     python_configurations = [
-        PythonConfiguration(version='2.7.17', arch="32", identifier='cp27-win32'),
-        PythonConfiguration(version='2.7.17', arch="64", identifier='cp27-win_amd64'),
-        PythonConfiguration(version='3.5.4', arch="32", identifier='cp35-win32'),
-        PythonConfiguration(version='3.5.4', arch="64", identifier='cp35-win_amd64'),
-        PythonConfiguration(version='3.6.8', arch="32", identifier='cp36-win32'),
-        PythonConfiguration(version='3.6.8', arch="64", identifier='cp36-win_amd64'),
-        PythonConfiguration(version='3.7.6', arch="32", identifier='cp37-win32'),
-        PythonConfiguration(version='3.7.6', arch="64", identifier='cp37-win_amd64'),
-        PythonConfiguration(version='3.8.1', arch="32", identifier='cp38-win32'),
-        PythonConfiguration(version='3.8.1', arch="64", identifier='cp38-win_amd64'),
+        PythonConfiguration(version='2.7.17', arch='32', identifier='cp27-win32', url=None),
+        PythonConfiguration(version='2.7.17', arch='64', identifier='cp27-win_amd64', url=None),
+        PythonConfiguration(version='3.5.4', arch='32', identifier='cp35-win32', url=None),
+        PythonConfiguration(version='3.5.4', arch='64', identifier='cp35-win_amd64', url=None),
+        PythonConfiguration(version='3.6.8', arch='32', identifier='cp36-win32', url=None),
+        PythonConfiguration(version='3.6.8', arch='64', identifier='cp36-win_amd64', url=None),
+        PythonConfiguration(version='3.7.6', arch='32', identifier='cp37-win32', url=None),
+        PythonConfiguration(version='3.7.6', arch='64', identifier='cp37-win_amd64', url=None),
+        PythonConfiguration(version='3.8.1', arch='32', identifier='cp38-win32', url=None),
+        PythonConfiguration(version='3.8.1', arch='64', identifier='cp38-win_amd64', url=None),
+        PythonConfiguration(version='2.7-v7.3.0', arch='32', identifier='pp27-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-win32.zip'),
+        PythonConfiguration(version='3.6-v7.3.0', arch='32', identifier='pp36-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-win32.zip'),
     ]
 
     if IS_RUNNING_ON_TRAVIS:
         # cannot install VCForPython27.msi which is needed for compiling C software
         # try with (and similar): msiexec /i VCForPython27.msi ALLUSERS=1 ACCEPT=YES /passive
-        python_configurations = [c for c in python_configurations if not c.version.startswith('2.7.')]
+        python_configurations = [c for c in python_configurations if not c.version.startswith('2.7')]
 
     # skip builds as required
     python_configurations = [c for c in python_configurations if build_selector(c.identifier)]
@@ -55,25 +74,35 @@ def get_python_configurations(build_selector):
     return python_configurations
 
 
+def extract_zip(zip_src, dest):
+    with ZipFile(zip_src) as zip:
+        zip.extractall(dest)
+
+
+def install_cpython(version, arch, nuget):
+    nuget_args = get_nuget_args(version, arch)
+    installation_path = os.path.join(nuget_args[-1], nuget_args[0] + '.' + version, 'tools')
+    simple_shell([nuget, 'install'] + nuget_args)
+    return installation_path
+
+
+def install_pypy(version, arch, url):
+    assert arch == '32'
+    # Inside the PyPy zip file is a directory with the same name
+    zip_filename = url.rsplit('/', 1)[-1]
+    installation_path = os.path.join('C:\\cibw', os.path.splitext(zip_filename)[0])
+    if not os.path.exists(installation_path):
+        pypy_zip = os.path.join('C:\\cibw', zip_filename)
+        download(url, pypy_zip)
+        # Extract to the parent directory because the zip file still contains a directory
+        extract_zip(pypy_zip, os.path.dirname(installation_path))
+        pypy_exe = 'pypy3.exe' if version[0] == '3' else 'pypy.exe'
+        simple_shell(['mklink', os.path.join(installation_path, 'python.exe'), os.path.join(installation_path, pypy_exe)])
+        simple_shell(['mklink', '/d', os.path.join(installation_path, 'Scripts'), os.path.join(installation_path, 'bin')])
+    return installation_path
+
+
 def build(project_dir, output_dir, test_command, test_requires, test_extras, before_build, build_verbosity, build_selector, repair_command, environment, dependency_constraints):
-    def simple_shell(args, env=None, cwd=None):
-        print('+ ' + ' '.join(args))
-        args = ['cmd', '/E:ON', '/V:ON', '/C'] + args
-        return subprocess.check_call(' '.join(args), env=env, cwd=cwd)
-
-    if IS_RUNNING_ON_AZURE or IS_RUNNING_ON_TRAVIS:
-        shell = simple_shell
-    else:
-        run_with_env = os.path.abspath(os.path.join(os.path.dirname(__file__), 'resources', 'appveyor_run_with_env.cmd'))
-
-        # run_with_env is a cmd file that sets the right environment variables
-        # to build on AppVeyor.
-        def shell(args, env=None, cwd=None):
-            # print the command executing for the logs
-            print('+ ' + ' '.join(args))
-            args = ['cmd', '/E:ON', '/V:ON', '/C', run_with_env] + args
-            return subprocess.check_call(' '.join(args), env=env, cwd=cwd)
-
     abs_project_dir = os.path.abspath(project_dir)
     temp_dir = tempfile.mkdtemp(prefix='cibuildwheel')
     built_wheel_dir = os.path.join(temp_dir, 'built_wheel')
@@ -86,17 +115,22 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
     python_configurations = get_python_configurations(build_selector)
     for config in python_configurations:
         # install Python
-        config_python_path = get_python_path(config)
-        simple_shell([nuget, "install"] + get_nuget_args(config))
-        assert os.path.exists(os.path.join(config_python_path, 'python.exe'))
+        if config.identifier.startswith('cp'):
+            installation_path = install_cpython(config.version, config.arch, nuget)
+        elif config.identifier.startswith('pp'):
+            installation_path = install_pypy(config.version, config.arch, config.url)
+        else:
+            raise ValueError("Unknown Python implementation")
+
+        assert os.path.exists(os.path.join(installation_path, 'python.exe'))
 
         # set up PATH and environment variables for run_with_env
         env = os.environ.copy()
         env['PYTHON_VERSION'] = config.version
         env['PYTHON_ARCH'] = config.arch
         env['PATH'] = os.pathsep.join([
-            config_python_path,
-            os.path.join(config_python_path, 'Scripts'),
+            installation_path,
+            os.path.join(installation_path, 'Scripts'),
             env['PATH']
         ])
         # update env with results from CIBW_ENVIRONMENT
@@ -105,7 +139,11 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
         # for the logs - check we're running the right version of python
         simple_shell(['where', 'python'], env=env)
         simple_shell(['python', '--version'], env=env)
-        simple_shell(['python', '-c', '"import struct; print(struct.calcsize(\'P\') * 8)\"'], env=env)
+        simple_shell(['python', '-c', '"import struct; print(struct.calcsize(\'P\') * 8)"'], env=env)
+        where_python = subprocess.check_output(['where', 'python'], env=env, universal_newlines=True).splitlines()[0].strip()
+        if where_python != os.path.join(installation_path, 'python.exe'):
+            print("cibuildwheel: python available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert python above it.", file=sys.stderr)
+            exit(1)
 
         dependency_constraint_flags = []
         if dependency_constraints:
@@ -114,9 +152,13 @@ def build(project_dir, output_dir, test_command, test_requires, test_extras, bef
             ]
 
         # make sure pip is installed
-        if not os.path.exists(os.path.join(config_python_path, 'Scripts', 'pip.exe')):
-            simple_shell(['python', get_pip_script] + dependency_constraint_flags, env=env, cwd="C:\\cibw")
-        assert os.path.exists(os.path.join(config_python_path, 'Scripts', 'pip.exe'))
+        if not os.path.exists(os.path.join(installation_path, 'Scripts', 'pip.exe')):
+            simple_shell(['python', get_pip_script], env=env, cwd="C:\\cibw")
+        assert os.path.exists(os.path.join(installation_path, 'Scripts', 'pip.exe'))
+        where_pip = subprocess.check_output(['where', 'pip'], env=env, universal_newlines=True).splitlines()[0].strip()
+        if where_pip.strip() != os.path.join(installation_path, 'Scripts', 'pip.exe'):
+            print("cibuildwheel: pip available on PATH doesn't match our installed instance. If you have modified PATH, ensure that you don't overwrite cibuildwheel's entry or insert pip above it.", file=sys.stderr)
+            exit(1)
 
         # prepare the Python environment
         simple_shell(['python', '-m', 'pip', 'install', '--upgrade', 'pip'] + dependency_constraint_flags, env=env)
diff --git a/docs/faq.md b/docs/faq.md
index dc424980..6f32da3f 100644
--- a/docs/faq.md
+++ b/docs/faq.md
@@ -22,7 +22,7 @@ Linux wheels are built in the [`manylinux` docker images](https://github.com/pyp
 
 - The project directory is mounted in the running Docker instance as `/project`, the output directory for the wheels as `/output`. In general, this is handled transparently by `cibuildwheel`. For a more finegrained level of control however, the root of the host file system is mounted as `/host`, allowing for example to access shared files, caches, etc. on the host file system.  Note that this is not available on CircleCI due to their Docker policies.
 
-- Alternative dockers images can be specified with the `CIBW_MANYLINUX_X86_64_IMAGE` and `CIBW_MANYLINUX_I686_IMAGE` options to allow for a custom, preconfigured build environment for the Linux builds. See [options](options.md#manylinux-image) for more details.
+- Alternative dockers images can be specified with the `CIBW_MANYLINUX_X86_64_IMAGE`, `CIBW_MANYLINUX_I686_IMAGE`, and `CIBW_MANYLINUX_PYPY_X86_64_IMAGE` options to allow for a custom, preconfigured build environment for the Linux builds. See [options](options.md#manylinux-image) for more details.
 
 ### Building packages with optional C extensions
 
@@ -37,3 +37,27 @@ myextension = Extension(
     optional=os.environ.get('CIBUILDWHEEL', '0') != '1',
 )
 ```
+
+### 'No module named XYZ' errors after running cibuildwheel on macOS
+
+`cibuildwheel` on Mac installs the distributions from Python.org system-wide during its operation. This is necessary, but it can cause some confusing errors after cibuildwheel has finished.
+
+Consider the build script:
+
+```bash
+python3 -m pip install twine cibuildwheel
+python3 -m cibuildwheel --output-dir wheelhouse
+python3 -m twine upload wheelhouse/*.whl
+# error: no module named 'twine'
+```
+
+This doesn't work because while `cibuildwheel` was running, it installed a few new versions of 'python3', so the `python3` run on line 3 isn't the same as the `python3` that ran on line 1.
+
+Solutions to this vary, but the simplest is to install tools immediately before they're used:
+
+```bash
+python3 -m pip install cibuildwheel
+python3 -m cibuildwheel --output-dir wheelhouse
+python3 -m pip install twine
+python3 -m twine upload wheelhouse/*.whl
+```
diff --git a/docs/options.md b/docs/options.md
index c2ba2c1d..0d827274 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -56,7 +56,7 @@ Default: `auto`
 
 `auto` will auto-detect platform using environment variables, such as `TRAVIS_OS_NAME`/`APPVEYOR`/`CIRCLECI`.
 
-For `linux` you need Docker running, on Mac or Linux. For `macos`, you need a Mac machine, and note that this script is going to automatically install MacPython on your system, so don't run on your development machine. For `windows`, you need to run in Windows, and it will build and test for all versions of Python at `C:\PythonXX[-x64]`.
+For `linux` you need Docker running, on macOS or Linux. For `macos`, you need a Mac machine, and note that this script is going to automatically install MacPython on your system, so don't run on your development machine. For `windows`, you need to run in Windows, and `cibuildwheel` will install required versions of Python to `C:\cibw\python` using NuGet.
 
 This option can also be set using the command-line option `--platform`.
 
@@ -68,21 +68,25 @@ Space-separated list of builds to build and skip. Each build has an identifier l
 
 When both options are specified, both conditions are applied and only builds with a tag that matches `CIBW_BUILD` and does not match `CIBW_SKIP` will be built.
 
-When setting the options, you can use shell-style globbing syntax (as per `fnmatch`). All the build identifiers supported by cibuildwheel are shown below:
+When setting the options, you can use shell-style globbing syntax (as per [`fnmatch`](https://docs.python.org/3/library/fnmatch.html)). All the build identifiers supported by cibuildwheel are shown below:
 
 <div class="build-id-table-marker"></div>
 
-|            | macOS 64bit        | Manylinux 64bit        | Manylinux 32bit      | Windows 64bit   | Windows 32bit  |
-|------------|--------------------|------------------------|----------------------|-----------------|----------------|
-| Python 2.7 | cp27-macosx_x86_64 | cp27-manylinux_x86_64  | cp27-manylinux_i686  | cp27-win_amd64  | cp27-win32     |
-| Python 3.5 | cp35-macosx_x86_64 | cp35-manylinux_x86_64  | cp35-manylinux_i686  | cp35-win_amd64  | cp35-win32     |
-| Python 3.6 | cp36-macosx_x86_64 | cp36-manylinux_x86_64  | cp36-manylinux_i686  | cp36-win_amd64  | cp36-win32     |
-| Python 3.7 | cp37-macosx_x86_64 | cp37-manylinux_x86_64  | cp37-manylinux_i686  | cp37-win_amd64  | cp37-win32     |
-| Python 3.8 | cp38-macosx_x86_64 | cp38-manylinux_x86_64  | cp38-manylinux_i686  | cp38-win_amd64  | cp38-win32     |
+|                 | macOS 64bit         | Manylinux x86 64bit    | Manylinux x86 32bit  | Windows 64bit   | Windows 32bit  | Manylinux Armv8 64bit  | Manylinux PPC64LE      | Manylinux s390x      |
+|-----------------|---------------------|------------------------|----------------------|-----------------|----------------|------------------------|------------------------|----------------------|
+| Python 2.7      | cp27-macosx_x86_64  | cp27-manylinux_x86_64  | cp27-manylinux_i686  | cp27-win_amd64  | cp27-win32     |                        |                        |                      |
+| Python 3.5      | cp35-macosx_x86_64  | cp35-manylinux_x86_64  | cp35-manylinux_i686  | cp35-win_amd64  | cp35-win32     | cp35-manylinux_aarch64 | cp35-manylinux_ppc64le | cp35-manylinux_s390x |
+| Python 3.6      | cp36-macosx_x86_64  | cp36-manylinux_x86_64  | cp36-manylinux_i686  | cp36-win_amd64  | cp36-win32     | cp36-manylinux_aarch64 | cp36-manylinux_ppc64le | cp36-manylinux_s390x |
+| Python 3.7      | cp37-macosx_x86_64  | cp37-manylinux_x86_64  | cp37-manylinux_i686  | cp37-win_amd64  | cp37-win32     | cp37-manylinux_aarch64 | cp37-manylinux_ppc64le | cp37-manylinux_s390x |
+| Python 3.8      | cp38-macosx_x86_64  | cp38-manylinux_x86_64  | cp38-manylinux_i686  | cp38-win_amd64  | cp38-win32     | cp38-manylinux_aarch64 | cp38-manylinux_ppc64le | cp38-manylinux_s390x |
+| PyPy 2.7 v7.3.0 | pp27-macosx_x86_64  | pp27-manylinux_x86_64  |                      |                 | pp27-win32     |                        |                        |                      |
+| PyPy 3.6 v7.3.0 | pp36-macosx_x86_64  | pp36-manylinux_x86_64  |                      |                 | pp36-win32     |                        |                        |                      |
 
 The list of supported and currently selected build identifiers can also be retrieved by passing the `--print-build-identifiers` flag to `cibuildwheel`.
 The format is `python_tag-platform_tag`, with tags similar to those in [PEP 425](https://www.python.org/dev/peps/pep-0425/#details).
 
+For CPython, the minimally supported macOS version is 10.9; for PyPy 2.7 and PyPy 3.6, respectively macOS 10.7 and 10.13 or higher is required.
+
 #### Examples
 
 ```yaml
@@ -113,6 +117,12 @@ CIBW_SKIP: cp36-manylinux*
 # Only build on Python 3 and skip 32-bit builds
 CIBW_BUILD: cp3?-*
 CIBW_SKIP: "*-win32 *-manylinux_i686"
+
+# Only build PyPy and CPython 3
+CIBW_BUILD: pp* cp3?-*
+
+# Disable building PyPy wheels on all platforms
+CIBW_SKIP: pp*
 ```
 
 <style>
@@ -235,16 +245,17 @@ CIBW_REPAIR_WHEEL_COMMAND_LINUX: "auditwheel repair --lib-sdir . -w {dest_dir} {
 ```
 
 
-### `CIBW_MANYLINUX_X86_64_IMAGE`, `CIBW_MANYLINUX_I686_IMAGE` {: #manylinux-image}
+### `CIBW_MANYLINUX_X86_64_IMAGE`, `CIBW_MANYLINUX_I686_IMAGE`, `CIBW_MANYLINUX_PYPY_X86_64_IMAGE`, `CIBW_MANYLINUX_AARCH64_IMAGE`, `CIBW_MANYLINUX_PPC64LE_IMAGE`, `CIBW_MANYLINUX_S390X_IMAGE` {: #manylinux-image}
 > Specify alternative manylinux docker images
 
-An alternative Docker image to be used for building [`manylinux`](https://github.com/pypa/manylinux) wheels. `cibuildwheel` will then pull these instead of the default images, [`quay.io/pypa/manylinux2010_x86_64`](https://quay.io/pypa/manylinux2010_x86_64) and [`quay.io/pypa/manylinux2010_i686`](https://quay.io/pypa/manylinux2010_i686).
+An alternative Docker image to be used for building [`manylinux`](https://github.com/pypa/manylinux) wheels. `cibuildwheel` will then pull these instead of the default images, [`quay.io/pypa/manylinux2010_x86_64`](https://quay.io/pypa/manylinux2010_x86_64), [`quay.io/pypa/manylinux2010_i686`](https://quay.io/pypa/manylinux2010_i686), [`pypywheels/manylinux2010-pypy_x86_64`](https://hub.docker.com/r/pypywheels/manylinux2010-pypy_x86_64), [`quay.io/pypa/manylinux2014_aarch64`](https://quay.io/pypa/manylinux2014_aarch64), [`quay.io/pypa/manylinux2014_ppc64le`](https://quay.io/pypa/manylinux2014_ppc64le), and [`quay.io/pypa/manylinux2014_s390x`](https://quay.io/pypa/manylinux2010_s390x).
 
-The value of this option can either be set to `manylinux1`, `manylinux2010` or `manylinux2014` to use a pinned version of the [official `manylinux` images](https://github.com/pypa/manylinux). Alternatively, set this options to any other valid Docker image name.
+The value of this option can either be set to `manylinux1`, `manylinux2010` or `manylinux2014` to use a pinned version of the [official `manylinux` images](https://github.com/pypa/manylinux) and [PyPy `manylinux` images](https://github.com/pypy/manylinux). Alternatively, set these options to any other valid Docker image name. Note that for PyPy, only the official `manylinux2010` image is currently available. For architectures other
+than x86 (x86\_64 and i686) manylinux2014 must be used because this is the first version of the manylinux specification that supports additional architectures.
 
-Beware to specify a valid Docker image that can be used in the same way as the official, default Docker images: all necessary Python and pip versions need to be present in `/opt/python/`, and the `auditwheel` tool needs to be present for `cibuildwheel` to work. Apart from that, the architecture and relevant shared system libraries need to be manylinux1-, manylinux2010- or manylinux2014-compatible in order to produce valid `manylinux1`/`manylinux2010`/`manylinux2014` wheels (see https://github.com/pypa/manylinux, [PEP 513](https://www.python.org/dev/peps/pep-0513/), [PEP 571](https://www.python.org/dev/peps/pep-0571/ and [PEP 599](https://www.python.org/dev/peps/pep-0599/) for more details).
+Beware to specify a valid Docker image that can be used in the same way as the official, default Docker images: all necessary Python and pip versions need to be present in `/opt/python/`, and the `auditwheel` tool needs to be present for `cibuildwheel` to work. Apart from that, the architecture and relevant shared system libraries need to be manylinux1-, manylinux2010- or manylinux2014-compatible in order to produce valid `manylinux1`/`manylinux2010`/`manylinux2014` wheels (see [pypa/manylinux on GitHub](https://github.com/pypa/manylinux), [PEP 513](https://www.python.org/dev/peps/pep-0513/), [PEP 571](https://www.python.org/dev/peps/pep-0571/) and [PEP 599](https://www.python.org/dev/peps/pep-0599/) for more details).
 
-Note that `auditwheel` detects the version of the `manylinux` standard in the Docker image through the `AUDITWHEEL_PLAT` environment variable, as `cibuildwheel` has no way of detecting the correct `--plat` command line argument to pass to `auditwheel` for a custom image. If a Docker image does not correctly set this `AUDITWHEEL_PLAT` environment variable, the `CIBW_ENVIRONMENT` option can be used to do so (e.g., `CIBW_ENVIRONMENT="manylinux2010_$(uname -m)"`).
+Note that `auditwheel` detects the version of the `manylinux` standard in the Docker image through the `AUDITWHEEL_PLAT` environment variable, as `cibuildwheel` has no way of detecting the correct `--plat` command line argument to pass to `auditwheel` for a custom image. If a Docker image does not correctly set this `AUDITWHEEL_PLAT` environment variable, the `CIBW_ENVIRONMENT` option can be used to do so (e.g., `CIBW_ENVIRONMENT='AUDITWHEEL_PLAT="manylinux2010_$(uname -m)"'`).
 
 Note that `manylinux2014` doesn't support builds with Python 2.7 - when building with `manylinux2014`, skip Python 2.7 using `CIBW_SKIP` (see example below).
 
@@ -252,8 +263,10 @@ Note that `manylinux2014` doesn't support builds with Python 2.7 - when building
 
 ```yaml
 # build using the manylinux1 image to ensure manylinux1 wheels are produced
+# skip PyPy, since there is no PyPy manylinux1 image
 CIBW_MANYLINUX_X86_64_IMAGE: manylinux1
 CIBW_MANYLINUX_I686_IMAGE: manylinux1
+CIBW_SKIP: pp*
 
 # build using the manylinux2014 image
 CIBW_MANYLINUX_X86_64_IMAGE: manylinux2014
diff --git a/examples/appveyor-minimal.yml b/examples/appveyor-minimal.yml
index b0503233..23f71e19 100644
--- a/examples/appveyor-minimal.yml
+++ b/examples/appveyor-minimal.yml
@@ -4,7 +4,7 @@ image:
 
 build_script:
   # windows
-  - cmd: pip install cibuildwheel==1.1.0
+  - cmd: pip3 install cibuildwheel==1.1.0
   - cmd: cibuildwheel --output-dir wheelhouse
   # linux
   - sh: "${HOME}/.localpython3.7.4/bin/python3 -m pip install cibuildwheel==1.1.0"
diff --git a/examples/azure-pipelines-minimal.yml b/examples/azure-pipelines-minimal.yml
index 567d6302..2e9a4311 100644
--- a/examples/azure-pipelines-minimal.yml
+++ b/examples/azure-pipelines-minimal.yml
@@ -4,19 +4,19 @@ jobs:
   steps:
     - task: UsePythonVersion@0
     - bash: |
-        python -m pip install --upgrade pip
-        pip install cibuildwheel==1.1.0
+        python3 -m pip install --upgrade pip
+        pip3 install cibuildwheel==1.1.0
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
 
 - job: macos
-  pool: {vmImage: 'macOS-10.13'}
+  pool: {vmImage: 'macOS-10.15'}
   steps:
     - task: UsePythonVersion@0
     - bash: |
-        python -m pip install --upgrade pip
-        pip install cibuildwheel==1.1.0
+        python3 -m pip install --upgrade pip
+        pip3 install cibuildwheel==1.1.0
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
@@ -28,8 +28,8 @@ jobs:
     - script: choco install vcpython27 -f -y
       displayName: Install Visual C++ for Python 2.7
     - bash: |
-        python -m pip install --upgrade pip
-        pip install cibuildwheel==1.1.0
+        python3 -m pip install --upgrade pip
+        pip3 install cibuildwheel==1.1.0
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
diff --git a/examples/circleci-minimal.yml b/examples/circleci-minimal.yml
index 053966d9..fd6c00e8 100644
--- a/examples/circleci-minimal.yml
+++ b/examples/circleci-minimal.yml
@@ -11,7 +11,7 @@ jobs:
       - run:
           name: Build the Linux wheels.
           command: |
-            pip install --user cibuildwheel==1.1.0
+            pip3 install --user cibuildwheel==1.1.0
             cibuildwheel --output-dir wheelhouse
       - store_artifacts:
           path: wheelhouse/
@@ -25,7 +25,7 @@ jobs:
       - run:
           name: Build the OS X wheels.
           command: |
-            pip install --user cibuildwheel==1.1.0
+            pip3 install --user cibuildwheel==1.1.0
             cibuildwheel --output-dir wheelhouse
       - store_artifacts:
           path: wheelhouse/
diff --git a/examples/travis-ci-deploy-only.yml b/examples/travis-ci-deploy-only.yml
index 55f8339b..1e7e55d5 100644
--- a/examples/travis-ci-deploy-only.yml
+++ b/examples/travis-ci-deploy-only.yml
@@ -23,12 +23,16 @@ env:
     # Note: TWINE_PASSWORD is set to a PyPI API token in Travis settings
 
 install:
-  - python -m pip install twine cibuildwheel==1.0.0
+  - python3 -m pip install cibuildwheel==1.1.0
 
 script:
   # build the wheels, put them into './wheelhouse'
-  - python -m cibuildwheel --output-dir wheelhouse
+  - python3 -m cibuildwheel --output-dir wheelhouse
 
 after_success:
   # if the release was tagged, upload them to PyPI
-  - if [[ $TRAVIS_TAG ]]; then python -m twine upload wheelhouse/*.whl; fi
+  - |
+    if [[ $TRAVIS_TAG ]]; then
+      python3 -m pip install twine
+      python3 -m twine upload wheelhouse/*.whl
+    fi
diff --git a/examples/travis-ci-minimal.yml b/examples/travis-ci-minimal.yml
index e71772b7..30356762 100644
--- a/examples/travis-ci-minimal.yml
+++ b/examples/travis-ci-minimal.yml
@@ -4,6 +4,15 @@ jobs:
   include:
     # perform a linux build
     - services: docker
+    # perform a linux ARMv8 build
+    - services: docker
+      arch: aarch64
+    # perform a linux PPC64LE build
+    - services: docker
+      arch: ppc64le
+    # perform a linux S390X build
+    - services: docker
+      arch: s390x
     # and a mac build
     - os: osx
       language: shell
@@ -15,8 +24,8 @@ jobs:
         - export PATH="/c/Python38:/c/Python38/Scripts:$PATH"
 
 install:
-  - python -m pip install cibuildwheel==1.1.0
+  - python3 -m pip install cibuildwheel==1.1.0
 
 script:
   # build the wheels, put them into './wheelhouse'
-  - python -m cibuildwheel --output-dir wheelhouse
+  - python3 -m cibuildwheel --output-dir wheelhouse
diff --git a/examples/travis-ci-test-and-deploy.yml b/examples/travis-ci-test-and-deploy.yml
index 006fe940..81b206dc 100644
--- a/examples/travis-ci-test-and-deploy.yml
+++ b/examples/travis-ci-test-and-deploy.yml
@@ -20,10 +20,10 @@ before_install:
     fi
 
 install:
-  - python -m pip install pytest
+  - python3 -m pip install pytest
 
 script:
-  - python setup.py install
+  - python3 setup.py install
   - pytest
 
 stages:
@@ -46,31 +46,39 @@ jobs:
     - stage: deploy
       name: Deploy source distribution
       install: skip
-      script: python setup.py sdist --formats=gztar
-      after_success: python -m twine upload --skip-existing dist/*.tar.gz
+      script: python3 setup.py sdist --formats=gztar
+      after_success: |
+        python3 -m pip install twine
+        python3 -m twine upload --skip-existing dist/*.tar.gz
     # Deploy on linux
     - stage: deploy
       name: Build and deploy Linux wheels
       services: docker
-      install: python -m pip install twine cibuildwheel==1.0.0
-      script: python -m cibuildwheel --output-dir wheelhouse
-      after_success: python -m twine upload --skip-existing wheelhouse/*.whl
+      install: python3 -m pip install cibuildwheel==1.1.0
+      script: python3 -m cibuildwheel --output-dir wheelhouse
+      after_success: |
+        python3 -m pip install twine
+        python3 -m twine upload --skip-existing wheelhouse/*.whl
     # Deploy on mac
     - stage: deploy
       name: Build and deploy macOS wheels
       os: osx
       language: shell
-      install: python -m pip install twine cibuildwheel==1.0.0
-      script: python -m cibuildwheel --output-dir wheelhouse
-      after_success: python -m twine upload --skip-existing wheelhouse/*.whl
+      install: python3 -m pip install cibuildwheel==1.1.0
+      script: python3 -m cibuildwheel --output-dir wheelhouse
+      after_success: |
+        python3 -m pip install twine
+        python3 -m twine upload --skip-existing wheelhouse/*.whl
     # Deploy on windows
     - stage: deploy
       name: Build and deploy Windows wheels
       os: windows
       language: shell
-      install: python -m pip install twine cibuildwheel==1.0.0
-      script: python -m cibuildwheel --output-dir wheelhouse
-      after_success: python -m twine upload --skip-existing wheelhouse/*.whl
+      install: python3 -m pip install cibuildwheel==1.1.0
+      script: python3 -m cibuildwheel --output-dir wheelhouse
+      after_success: |
+        python3 -m pip install twine
+        python3 -m twine upload --skip-existing wheelhouse/*.whl
 
 env:
   global:
diff --git a/test/01_basic/cibuildwheel_test.py b/test/01_basic/cibuildwheel_test.py
index 76dd4857..51875a8a 100644
--- a/test/01_basic/cibuildwheel_test.py
+++ b/test/01_basic/cibuildwheel_test.py
@@ -1,4 +1,5 @@
 import os
+import platform
 
 import utils
 
@@ -20,7 +21,10 @@ def test_build_identifiers():
     # after adding CIBW_MANYLINUX_IMAGE to support manylinux2010, there
     # can be multiple wheels for each wheel, though, so we need to limit
     # the expected wheels
-    expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0')
-                       if '-manylinux' not in w or '-manylinux1' in w]
+    if platform.machine() in ['x86_64', 'i686']:
+        expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0')
+                           if '-manylinux' not in w or '-manylinux1' in w]
+    else:
+        expected_wheels = utils.expected_wheels('spam', '0.1.0')
     build_identifiers = utils.cibuildwheel_get_build_identifiers(project_dir)
     assert len(expected_wheels) == len(build_identifiers)
diff --git a/test/05_environment/cibuildwheel_test.py b/test/05_environment/cibuildwheel_test.py
index 4f0b922d..ab467111 100644
--- a/test/05_environment/cibuildwheel_test.py
+++ b/test/05_environment/cibuildwheel_test.py
@@ -1,5 +1,6 @@
 import os
-
+import pytest
+import subprocess
 import utils
 
 
@@ -17,3 +18,15 @@ def test():
     # also check that we got the right wheels built
     expected_wheels = utils.expected_wheels('spam', '0.1.0')
     assert set(actual_wheels) == set(expected_wheels)
+
+
+def test_overridden_path(tmp_path):
+    project_dir = os.path.dirname(__file__)
+
+    # mess up PATH, somehow
+    with pytest.raises(subprocess.CalledProcessError):
+        utils.cibuildwheel_run(project_dir, output_dir=tmp_path, add_env={
+            'CIBW_ENVIRONMENT': '''SOMETHING="$(mkdir new_path && touch new_path/python)" PATH="$(realpath new_path):$PATH"''',
+            'CIBW_ENVIRONMENT_WINDOWS': '''SOMETHING="$(mkdir new_path && type nul > new_path/python.exe)" PATH="$CD\\new_path;$PATH"''',
+        })
+    assert len(os.listdir(str(tmp_path))) == 0
diff --git a/test/06_docker_images/cibuildwheel_test.py b/test/06_docker_images/cibuildwheel_test.py
index 9f243664..7be4a4c3 100644
--- a/test/06_docker_images/cibuildwheel_test.py
+++ b/test/06_docker_images/cibuildwheel_test.py
@@ -1,4 +1,5 @@
 import os
+import platform
 
 import pytest
 
@@ -10,12 +11,16 @@ def test():
 
     if utils.platform != 'linux':
         pytest.skip('the test is only relevant to the linux build')
+    if platform.machine() not in ['x86_64', 'i686']:
+        pytest.skip('this test is currently only possible on x86_64/i686 due to availability of alternative images')
 
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env={
         'CIBW_MANYLINUX_X86_64_IMAGE': 'dockcross/manylinux2010-x64',
         'CIBW_MANYLINUX_I686_IMAGE': 'dockcross/manylinux2010-x86',
+        'CIBW_SKIP': 'pp*',
     })
 
     # also check that we got the right wheels built
-    expected_wheels = utils.expected_wheels('spam', '0.1.0')
+    expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0')
+                       if '-pp' not in w]
     assert set(actual_wheels) == set(expected_wheels)
diff --git a/test/08_manylinuxXXXX_only/cibuildwheel_test.py b/test/08_manylinuxXXXX_only/cibuildwheel_test.py
index 439f428f..9abdc129 100644
--- a/test/08_manylinuxXXXX_only/cibuildwheel_test.py
+++ b/test/08_manylinuxXXXX_only/cibuildwheel_test.py
@@ -1,4 +1,5 @@
 import os
+import platform
 
 import pytest
 
@@ -11,6 +12,9 @@ def test(manylinux_image):
 
     if utils.platform != 'linux':
         pytest.skip('the docker test is only relevant to the linux build')
+    elif platform.machine not in ['x86_64', 'i686']:
+        if manylinux_image in ['manylinux1', 'manylinux2010']:
+            pytest.skip("manylinux1 and 2010 doesn't exist for non-x86 architectures")
 
     # build the wheels
     # CFLAGS environment variable is necessary to fail on 'malloc_info' (on manylinux1) during compilation/linking,
@@ -19,12 +23,22 @@ def test(manylinux_image):
         'CIBW_ENVIRONMENT': 'CFLAGS="$CFLAGS -Werror=implicit-function-declaration"',
         'CIBW_MANYLINUX_X86_64_IMAGE': manylinux_image,
         'CIBW_MANYLINUX_I686_IMAGE': manylinux_image,
+        'CIBW_MANYLINUX_PYPY_X86_64_IMAGE': manylinux_image,
+        'CIBW_MANYLINUX_AARCH64_IMAGE': manylinux_image,
+        'CIBW_MANYLINUX_PPC64LE_IMAGE': manylinux_image,
+        'CIBW_MANYLINUX_S390X_IMAGE': manylinux_image,
     }
-    if manylinux_image == 'manylinux2014':
-        add_env['CIBW_SKIP'] = 'cp27*'  # not available on manylinux2014
+    if manylinux_image == 'manylinux1':
+        # We don't have a manylinux1 image for PyPy
+        add_env['CIBW_SKIP'] = 'pp*'
+    elif manylinux_image == 'manylinux2014':
+        # We don't have a manylinux2014 image for PyPy (yet?)
+        add_env['CIBW_SKIP'] = 'cp27* pp*'  # Python 2.7 not available on manylinux2014
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
 
     expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0', manylinux_versions=[manylinux_image])]
     if manylinux_image == 'manylinux2014':
         expected_wheels = [w for w in expected_wheels if '-cp27' not in w]
+    if manylinux_image in ['manylinux1', 'manylinux2014']:
+        expected_wheels = [w for w in expected_wheels if '-pp' not in w]
     assert set(actual_wheels) == set(expected_wheels)
diff --git a/test/10_cpp_standards/cibuildwheel_test.py b/test/10_cpp_standards/cibuildwheel_test.py
index 9b2cb724..cf838800 100644
--- a/test/10_cpp_standards/cibuildwheel_test.py
+++ b/test/10_cpp_standards/cibuildwheel_test.py
@@ -10,22 +10,23 @@ project_dir = os.path.dirname(__file__)
 def test_cpp11(tmp_path):
     # This test checks that the C++11 standard is supported
 
-    add_env = {'CIBW_SKIP': 'cp27-win*', 'CIBW_ENVIRONMENT': 'STANDARD=11'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32', 'CIBW_ENVIRONMENT': 'STANDARD=11'}
     # VC++ for Python 2.7 does not support modern standards
     if utils.platform == 'macos':
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.9'
 
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
-    expected_wheels = [x for x in utils.expected_wheels(
+    expected_wheels = [w for w in utils.expected_wheels(
         'spam', '0.1.0', macosx_deployment_target='10.9')
-        if 'cp27-cp27m-win' not in x]
+        if 'cp27-cp27m-win' not in w
+        and 'pp27-pypy_73-win32' not in w]
     assert set(actual_wheels) == set(expected_wheels)
 
 
 def test_cpp14():
     # This test checks that the C++14 standard is supported
 
-    add_env = {'CIBW_SKIP': 'cp27-win* cp35-win*', 'CIBW_ENVIRONMENT': 'STANDARD=14'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32 cp35-win*', 'CIBW_ENVIRONMENT': 'STANDARD=14'}
     # VC++ for Python 2.7 does not support modern standards
     # The manylinux1 docker image does not have a compiler which supports C++11
     # Python 3.4 and 3.5 are compiled with MSVC 10, which does not support C++14
@@ -33,27 +34,32 @@ def test_cpp14():
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.9'
 
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
-    expected_wheels = [x for x in utils.expected_wheels(
+    expected_wheels = [w for w in utils.expected_wheels(
         'spam', '0.1.0', macosx_deployment_target='10.9')
-        if 'cp27-cp27m-win' not in x and 'cp35-cp35m-win' not in x]
+        if 'cp27-cp27m-win' not in w
+        and 'pp27-pypy_73-win32' not in w
+        and 'cp35-cp35m-win' not in w]
     assert set(actual_wheels) == set(expected_wheels)
 
 
 def test_cpp17():
     # This test checks that the C++17 standard is supported
 
-    # Python 2.7 uses the `register` keyword which is forbidden in the C++17 standard
+    # Python and PyPy 2.7 use the `register` keyword which is forbidden in the C++17 standard
     # The manylinux1 docker image does not have a compiler which supports C++11
-    # Python 3.4 and 3.5 are compiled with MSVC 10, which does not support C++17
+    # Python 3.5 and PyPy 3.6 are compiled with MSVC 10, which does not support C++17
     if os.environ.get('APPVEYOR_BUILD_WORKER_IMAGE', '') == 'Visual Studio 2015':
         pytest.skip('Visual Studio 2015 does not support C++17')
 
-    add_env = {'CIBW_SKIP': 'cp27-win* cp35-win*', 'CIBW_ENVIRONMENT': 'STANDARD=17'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32 cp35-win* pp36-win32', 'CIBW_ENVIRONMENT': 'STANDARD=17'}
     if utils.platform == 'macos':
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.13'
 
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
-    expected_wheels = [x for x in utils.expected_wheels(
+    expected_wheels = [w for w in utils.expected_wheels(
         'spam', '0.1.0', macosx_deployment_target='10.13')
-        if 'cp27-cp27m-win' not in x and 'cp35-cp35m-win' not in x]
+        if 'cp27-cp27m-win' not in w
+        and 'pp27-pypy_73-win32' not in w
+        and 'cp35-cp35m-win' not in w
+        and 'pp36-pypy36_pp73-win32' not in w]
     assert set(actual_wheels) == set(expected_wheels)
diff --git a/test/shared/utils.py b/test/shared/utils.py
index 4d6b96d0..862d4466 100644
--- a/test/shared/utils.py
+++ b/test/shared/utils.py
@@ -5,6 +5,7 @@ This file is added to the PYTHONPATH in the test runner at bin/run_test.py.
 '''
 
 import os
+import platform as pm
 import shutil
 import subprocess
 import sys
@@ -70,7 +71,7 @@ def cibuildwheel_run(project_path, env=None, add_env=None, output_dir=None):
     return wheels
 
 
-def expected_wheels(package_name, package_version, manylinux_versions=['manylinux1', 'manylinux2010'],
+def expected_wheels(package_name, package_version, manylinux_versions=None,
                     macosx_deployment_target=None):
     '''
     Returns a list of expected wheels from a run of cibuildwheel.
@@ -79,29 +80,45 @@ def expected_wheels(package_name, package_version, manylinux_versions=['manylinu
     # {distribution}-{version}(-{build tag})?-{python tag}-{abi tag}-{platform tag}.whl
     # {python tag} and {abi tag} are closely related to the python interpreter used to build the wheel
     # so we'll merge them below as python_abi_tag
-    python_abi_tags = ['cp27-cp27m', 'cp35-cp35m', 'cp36-cp36m', 'cp37-cp37m', 'cp38-cp38']
+
+    python_abi_tags = ['cp35-cp35m', 'cp36-cp36m', 'cp37-cp37m', 'cp38-cp38']
+    extra_x86_python_abi_tags = ['cp27-cp27m', 'pp27-pypy_73', 'pp36-pypy36_pp73']
+
     if platform == 'linux':
-        python_abi_tags.append('cp27-cp27mu')  # python 2.7 has 2 different ABI on manylinux
-        platform_tags = []
-        for architecture in ['x86_64', 'i686']:
-            for manylinux_version in manylinux_versions:
-                platform_tags.append('{manylinux_version}_{architecture}'.format(
-                    manylinux_version=manylinux_version, architecture=architecture
-                ))
+        if pm.machine() not in ['x86_64', 'i686']:
+            if manylinux_versions is None:
+                manylinux_versions = ['manylinux2014']
+            architectures = {'cp': [pm.machine()]}
+        else:
+            if manylinux_versions is None:
+                manylinux_versions = ['manylinux1', 'manylinux2010']
+            python_abi_tags += extra_x86_python_abi_tags
+            python_abi_tags.append('cp27-cp27mu')  # python 2.7 has 2 different ABI on manylinux
+            architectures = {'cp': ['x86_64', 'i686'], 'pp': ['x86_64']}
+        platform_tags = {}
+        for python_implemention in architectures:
+            platform_tags[python_implemention] = [
+                '{manylinux_version}_{architecture}'.format(
+                    manylinux_version=manylinux_version, architecture=architecture)
+                for architecture in architectures[python_implemention]
+                for manylinux_version in manylinux_versions
+            ]
 
         def get_platform_tags(python_abi_tag):
-            return platform_tags
-
+            return platform_tags[python_abi_tag[:2]]
     elif platform == 'windows':
+        python_abi_tags += extra_x86_python_abi_tags
+        platform_tags = {'cp': ['win32', 'win_amd64'], 'pp': ['win32']}
 
         def get_platform_tags(python_abi_tag):
-            return ['win32', 'win_amd64']
+            return platform_tags[python_abi_tag[:2]]
 
     elif platform == 'macos':
+        python_abi_tags += extra_x86_python_abi_tags
 
         def get_platform_tags(python_abi_tag):
-            return ['macosx_' + (macosx_deployment_target or "10.9").replace(".", "_") + '_x86_64']
-
+            default_version = '10.7' if python_abi_tag.startswith('pp') else '10.9'
+            return ['macosx_{}_x86_64'.format((macosx_deployment_target or default_version).replace('.', '_'))]
     else:
         raise Exception('unsupported platform')
 
@@ -115,7 +132,7 @@ def expected_wheels(package_name, package_version, manylinux_versions=['manylinu
 
     if IS_WINDOWS_RUNNING_ON_TRAVIS:
         # Python 2.7 isn't supported on Travis.
-        templates = [t for t in templates if '-cp27-' not in t]
+        templates = [t for t in templates if '-cp27-' not in t and '-pp2' not in t]
 
     return templates
 
diff --git a/unit_test/main_tests/main_options_test.py b/unit_test/main_tests/main_options_test.py
index 89cf5840..9acb408b 100644
--- a/unit_test/main_tests/main_options_test.py
+++ b/unit_test/main_tests/main_options_test.py
@@ -68,6 +68,11 @@ def test_build_selector(platform, intercepted_build_args, monkeypatch):
     ('i686', 'manylinux2010', 'quay.io/pypa/manylinux2010_i686:*'),
     ('i686', 'manylinux2014', 'quay.io/pypa/manylinux2014_i686:*'),
     ('i686', 'custom_image', 'custom_image'),
+    ('pypy_x86_64', None, 'pypywheels/manylinux2010-pypy_x86_64'),
+    ('pypy_x86_64', 'manylinux1', 'manylinux1'),  # Does not exist
+    ('pypy_x86_64', 'manylinux2010', 'pypywheels/manylinux2010-pypy_x86_64'),
+    ('pypy_x86_64', 'manylinux2014', 'manylinux2014'),  # Does not exist (yet)
+    ('pypy_x86_64', 'custom_image', 'custom_image'),
 ])
 def test_manylinux_images(architecture, image, full_image, platform, intercepted_build_args, monkeypatch):
     if image is not None: