diff --git a/CI.md b/CI.md
index 1b7c3552..69a2b3bd 100644
--- a/CI.md
+++ b/CI.md
@@ -1,11 +1,12 @@
 This is a summary of the Python versions and platforms covered by the different CI platforms:
 
-|          | 3.6                          | 3.7                                               | 3.8              |
-|----------|------------------------------|---------------------------------------------------|------------------|
-| Linux    | Travis CI / CircleCI         | AppVeyor / GitHub Actions                         | Azure Pipelines  |
-| macOS    | CircleCI                     | AppVeyor / Travis CI¹ / CircleCI / GitHub Actions  | Azure Pipelines  |
-| Windows  | Travis CI / Azure Pipelines  | AppVeyor / GitHub Actions                         | Azure Pipelines  |
+|          | 3.5              | 3.6              | 3.7                                                | 3.8              |
+|----------|------------------|------------------|----------------------------------------------------|------------------|
+| Linux    | Travis CI        | CircleCI         | AppVeyor² / GitHub Actions                         | Azure Pipelines  |
+| macOS    | Azure Pipelines  | CircleCI         | AppVeyor² / Travis CI¹ / CircleCI / GitHub Actions | Azure Pipelines  |
+| Windows  | TravisCI         | Azure Pipelines  | AppVeyor² / GitHub Actions                         | Azure Pipelines  |
 
 > ¹ Python version not really pinned, but dependent on the (default) version of image used.
+> ² AppVeyor only runs the "basic" test to reduce load.
 
 Non-x86 architectures are covered on Travis CI using Python 3.6.
diff --git a/README.md b/README.md
index a1a2b95c..28ebbf4f 100644
--- a/README.md
+++ b/README.md
@@ -77,7 +77,7 @@ env:
     # Note: TWINE_PASSWORD is set to a PyPI API token in Travis settings
 
 install:
-  - python3 -m pip install cibuildwheel==1.3.0
+  - python3 -m pip install cibuildwheel==1.4.1
 
 script:
   # build the wheels, put them into './wheelhouse'
@@ -128,6 +128,9 @@ Here are some repos that use cibuildwheel.
 - [Twisted](https://github.com/twisted/twisted)
 - [gmic-py](https://github.com/dtschump/gmic-py)
 - [creme](https://github.com/creme-ml/creme)
+- [PyAV](https://github.com/PyAV-Org/PyAV)
+- [aiortc](https://github.com/aiortc/aiortc)
+- [aioquic](https://github.com/aiortc/aioquic)
 
 > Add your repo here! Send a PR.
 
@@ -143,6 +146,44 @@ This is similar to static linking, so it might have some licence implications. C
 Changelog
 =========
 
+### 1.4.1
+
+_4 May 2020_
+
+- 🐛 Fix a bug causing programs running inside the i686 manylinux images to
+  think they were running x86_64 and target the wrong architecture. (#336,
+  #338)
+
+### 1.4.0
+
+_2 May 2020_
+
+- ✨ Deterministic builds. cibuildwheel now locks the versions of the tools it
+  uses. This means that pinning your version of cibuildwheel pins the versions
+  of pip, setuptools, manylinux etc. that are used under the hood. This should
+  make things more reliable. But note that we don't control the entire build
+  environment on macOS and Windows, where the version of Xcode and Visual
+  Studio can still effect things.
+
+  This can be controlled using the [CIBW_DEPENDENCY_VERSIONS](https://cibuildwheel.readthedocs.io/en/stable/options/#dependency-versions)
+  and [manylinux image](https://cibuildwheel.readthedocs.io/en/stable/options/#manylinux-image)
+  options - if you always want to use the latest toolchain, you can still do
+  that, or you can specify your own pip constraints file and manylinux image.
+  (#256)
+- ✨ Added `package_dir` command line option, meaning we now support building
+  a package that lives in a subdirectory and pulls in files from the wider
+  project. See [the `package_dir` option help](https://cibuildwheel.readthedocs.io/en/stable/options/#command-line-options)
+  for more information.
+
+  Note that this change makes the working directory (where you call
+  cibuildwheel from) relevant on Linux, as it's considered the 'project' and
+  will be copied into the Docker container. If your builds are slower on this
+  version, that's likely the reason. `cd` to your project and then call
+  `cibuildwheel` from there. (#319, #295)
+- 🛠 On macOS, we make `MACOSX_DEPLOYMENT_TARGET` default to `10.9` if it's
+  not set. This should make things more consistent between Python versions.
+- 🛠 Dependency updates - CPython 3.7.7, CPython 2.7.18, Pypy 7.3.1.
+
 ### 1.3.0
 
 _12 March 2020_
diff --git a/cibuildwheel/__init__.py b/cibuildwheel/__init__.py
index 19b4f1d6..8e3c933c 100644
--- a/cibuildwheel/__init__.py
+++ b/cibuildwheel/__init__.py
@@ -1 +1 @@
-__version__ = '1.3.0'
+__version__ = '1.4.1'
diff --git a/cibuildwheel/linux.py b/cibuildwheel/linux.py
index 04b2a620..d30635c3 100644
--- a/cibuildwheel/linux.py
+++ b/cibuildwheel/linux.py
@@ -109,6 +109,7 @@ def build(options: BuildOptions):
         container_name = 'cibuildwheel-{}'.format(uuid.uuid4())
 
         try:
+            shell_cmd = ['linux32', '/bin/bash'] if platform_tag.endswith("i686") else ['/bin/bash']
             call(['docker', 'create',
                   '--env', 'CIBUILDWHEEL',
                   '--name', container_name,
@@ -136,7 +137,7 @@ def build(options: BuildOptions):
                         )
 
                 call(
-                    ['docker', 'exec', '-i', container_name, '/bin/bash'],
+                    ['docker', 'exec', '-i', container_name] + shell_cmd,
                     universal_newlines=True,
                     input='''
                         # give xtrace output an extra level of indent inside docker
@@ -266,7 +267,7 @@ def build(options: BuildOptions):
                   container_name + ':/output/.',
                   os.path.abspath(options.output_dir)])
         except subprocess.CalledProcessError as error:
-            troubleshoot(options.project_dir, error)
+            troubleshoot(options.package_dir, error)
             exit(1)
         finally:
             # Still gets executed, even when 'exit(1)' gets called
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 599e9b23..8eb7984c 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -30,14 +30,14 @@ def get_python_configurations(build_selector):
     PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'identifier', 'url'])
     python_configurations = [
         # CPython
-        PythonConfiguration(version='2.7', identifier='cp27-macosx_x86_64', url='https://www.python.org/ftp/python/2.7.17/python-2.7.17-macosx10.9.pkg'),
+        PythonConfiguration(version='2.7', identifier='cp27-macosx_x86_64', url='https://www.python.org/ftp/python/2.7.18/python-2.7.18-macosx10.9.pkg'),
         PythonConfiguration(version='3.5', identifier='cp35-macosx_x86_64', url='https://www.python.org/ftp/python/3.5.4/python-3.5.4-macosx10.6.pkg'),
         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='3.7', identifier='cp37-macosx_x86_64', url='https://www.python.org/ftp/python/3.7.7/python-3.7.7-macosx10.9.pkg'),
         PythonConfiguration(version='3.8', identifier='cp38-macosx_x86_64', url='https://www.python.org/ftp/python/3.8.2/python-3.8.2-macosx10.9.pkg'),
         # PyPy
-        PythonConfiguration(version='2.7', identifier='pp27-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-osx64.tar.bz2'),
-        PythonConfiguration(version='3.6', identifier='pp36-macosx_x86_64', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-osx64.tar.bz2'),
+        PythonConfiguration(version='2.7', identifier='pp27-macosx_x86_64', url='https://downloads.python.org/pypy/pypy2.7-v7.3.1-osx64.tar.bz2'),
+        PythonConfiguration(version='3.6', identifier='pp36-macosx_x86_64', url='https://downloads.python.org/pypy/pypy3.6-v7.3.1-osx64.tar.bz2'),
     ]
 
     # skip builds as required
@@ -74,7 +74,7 @@ def install_cpython(version, url):
         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
+            open_ssl_patch_url = 'https://github.com/mayeut/patch-macos-python-openssl/releases/download/v1.0.2u/patch-macos-python-%s-openssl-v1.0.2u.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'])
 
@@ -95,12 +95,6 @@ def install_pypy(version, url):
         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 "-v7.3.0-" in url 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'
diff --git a/cibuildwheel/resources/constraints-python27.txt b/cibuildwheel/resources/constraints-python27.txt
index 0154cf81..6da3b134 100644
--- a/cibuildwheel/resources/constraints-python27.txt
+++ b/cibuildwheel/resources/constraints-python27.txt
@@ -2,7 +2,7 @@
 # This file is autogenerated by pip-compile
 # To update, run:
 #
-#    bin/update_constraints
+#    bin/update_constraints.py
 #
 appdirs==1.4.3            # via virtualenv
 configparser==4.0.2       # via importlib-metadata
@@ -10,17 +10,17 @@ contextlib2==0.6.0.post1  # via importlib-metadata, importlib-resources, virtual
 delocate==0.8.0           # via -r cibuildwheel/resources/constraints.in
 distlib==0.3.0            # via virtualenv
 filelock==3.0.12          # via virtualenv
-importlib-metadata==1.5.0  # via importlib-resources, virtualenv
-importlib-resources==1.3.1  # via virtualenv
+importlib-metadata==1.6.0  # via importlib-resources, virtualenv
+importlib-resources==1.5.0  # via virtualenv
 pathlib2==2.3.5           # via importlib-metadata, importlib-resources, virtualenv
 scandir==1.10.0           # via pathlib2
 singledispatch==3.4.0.3   # via importlib-resources
 six==1.14.0               # via pathlib2, virtualenv
 typing==3.7.4.1           # via importlib-resources
-virtualenv==20.0.10       # via -r cibuildwheel/resources/constraints.in
+virtualenv==20.0.18       # via -r cibuildwheel/resources/constraints.in
 wheel==0.34.2             # via -r cibuildwheel/resources/constraints.in, delocate
 zipp==1.2.0               # via importlib-metadata, importlib-resources
 
 # The following packages are considered to be unsafe in a requirements file:
-pip==20.0.2               # via -r cibuildwheel/resources/constraints.in
-setuptools==44.0.0        # via -r cibuildwheel/resources/constraints.in
+pip==20.1                 # via -r cibuildwheel/resources/constraints.in
+setuptools==44.1.0        # via -r cibuildwheel/resources/constraints.in
diff --git a/cibuildwheel/resources/constraints-python35.txt b/cibuildwheel/resources/constraints-python35.txt
index e6d35c5d..70591458 100644
--- a/cibuildwheel/resources/constraints-python35.txt
+++ b/cibuildwheel/resources/constraints-python35.txt
@@ -2,19 +2,19 @@
 # This file is autogenerated by pip-compile
 # To update, run:
 #
-#    bin/update_constraints
+#    bin/update_constraints.py
 #
 appdirs==1.4.3            # via virtualenv
 delocate==0.8.0           # via -r cibuildwheel/resources/constraints.in
 distlib==0.3.0            # via virtualenv
 filelock==3.0.12          # via virtualenv
-importlib-metadata==1.5.0  # via importlib-resources, virtualenv
-importlib-resources==1.3.1  # via virtualenv
+importlib-metadata==1.6.0  # via importlib-resources, virtualenv
+importlib-resources==1.5.0  # via virtualenv
 six==1.14.0               # via virtualenv
-virtualenv==20.0.10       # via -r cibuildwheel/resources/constraints.in
+virtualenv==20.0.18       # via -r cibuildwheel/resources/constraints.in
 wheel==0.34.2             # via -r cibuildwheel/resources/constraints.in, delocate
 zipp==1.2.0               # via importlib-metadata, importlib-resources
 
 # The following packages are considered to be unsafe in a requirements file:
-pip==20.0.2               # via -r cibuildwheel/resources/constraints.in
-setuptools==46.0.0        # via -r cibuildwheel/resources/constraints.in
+pip==20.1                 # via -r cibuildwheel/resources/constraints.in
+setuptools==46.1.3        # via -r cibuildwheel/resources/constraints.in
diff --git a/cibuildwheel/resources/constraints-python36.txt b/cibuildwheel/resources/constraints-python36.txt
index 1a0aa5a3..58776947 100644
--- a/cibuildwheel/resources/constraints-python36.txt
+++ b/cibuildwheel/resources/constraints-python36.txt
@@ -2,19 +2,19 @@
 # This file is autogenerated by pip-compile
 # To update, run:
 #
-#    bin/update_constraints
+#    bin/update_constraints.py
 #
 appdirs==1.4.3            # via virtualenv
 delocate==0.8.0           # via -r cibuildwheel/resources/constraints.in
 distlib==0.3.0            # via virtualenv
 filelock==3.0.12          # via virtualenv
-importlib-metadata==1.5.0  # via importlib-resources, virtualenv
-importlib-resources==1.3.1  # via virtualenv
+importlib-metadata==1.6.0  # via importlib-resources, virtualenv
+importlib-resources==1.5.0  # via virtualenv
 six==1.14.0               # via virtualenv
-virtualenv==20.0.10       # via -r cibuildwheel/resources/constraints.in
+virtualenv==20.0.18       # via -r cibuildwheel/resources/constraints.in
 wheel==0.34.2             # via -r cibuildwheel/resources/constraints.in, delocate
 zipp==3.1.0               # via importlib-metadata, importlib-resources
 
 # The following packages are considered to be unsafe in a requirements file:
-pip==20.0.2               # via -r cibuildwheel/resources/constraints.in
-setuptools==46.0.0        # via -r cibuildwheel/resources/constraints.in
+pip==20.1                 # via -r cibuildwheel/resources/constraints.in
+setuptools==46.1.3        # via -r cibuildwheel/resources/constraints.in
diff --git a/cibuildwheel/resources/constraints.txt b/cibuildwheel/resources/constraints.txt
index fd9e3eab..a9389c61 100644
--- a/cibuildwheel/resources/constraints.txt
+++ b/cibuildwheel/resources/constraints.txt
@@ -2,18 +2,18 @@
 # This file is autogenerated by pip-compile
 # To update, run:
 #
-#    bin/update_constraints
+#    bin/update_constraints.py
 #
 appdirs==1.4.3            # via virtualenv
 delocate==0.8.0           # via -r cibuildwheel/resources/constraints.in
 distlib==0.3.0            # via virtualenv
 filelock==3.0.12          # via virtualenv
-importlib-metadata==1.5.0  # via virtualenv
+importlib-metadata==1.6.0  # via virtualenv
 six==1.14.0               # via virtualenv
-virtualenv==20.0.10       # via -r cibuildwheel/resources/constraints.in
+virtualenv==20.0.18       # via -r cibuildwheel/resources/constraints.in
 wheel==0.34.2             # via -r cibuildwheel/resources/constraints.in, delocate
 zipp==3.1.0               # via importlib-metadata
 
 # The following packages are considered to be unsafe in a requirements file:
-pip==20.0.2               # via -r cibuildwheel/resources/constraints.in
-setuptools==46.0.0        # via -r cibuildwheel/resources/constraints.in
+pip==20.1                 # via -r cibuildwheel/resources/constraints.in
+setuptools==46.1.3        # via -r cibuildwheel/resources/constraints.in
diff --git a/cibuildwheel/resources/pinned_docker_images.cfg b/cibuildwheel/resources/pinned_docker_images.cfg
index 7cbcab64..bf161d3e 100644
--- a/cibuildwheel/resources/pinned_docker_images.cfg
+++ b/cibuildwheel/resources/pinned_docker_images.cfg
@@ -1,22 +1,22 @@
 [x86_64]
-manylinux1 = quay.io/pypa/manylinux1_x86_64:2020-03-07-9c5ba95
-manylinux2010 = quay.io/pypa/manylinux2010_x86_64:2020-03-07-1825e8f
-manylinux2014 = quay.io/pypa/manylinux2014_x86_64:2020-03-07-06139da
+manylinux1 = quay.io/pypa/manylinux1_x86_64:2020-04-25-37c204c
+manylinux2010 = quay.io/pypa/manylinux2010_x86_64:2020-04-29-0e1afc5
+manylinux2014 = quay.io/pypa/manylinux2014_x86_64:2020-05-01-b37d76b
 
 [i686]
-manylinux1 = quay.io/pypa/manylinux1_i686:2020-03-07-9c5ba95
-manylinux2010 = quay.io/pypa/manylinux2010_i686:2020-03-07-1825e8f
-manylinux2014 = quay.io/pypa/manylinux2014_i686:2020-03-07-06139da
+manylinux1 = quay.io/pypa/manylinux1_i686:2020-04-25-37c204c
+manylinux2010 = quay.io/pypa/manylinux2010_i686:2020-04-29-0e1afc5
+manylinux2014 = quay.io/pypa/manylinux2014_i686:2020-05-01-b37d76b
 
 [pypy_x86_64]
-manylinux2010 = pypywheels/manylinux2010-pypy_x86_64:latest
+manylinux2010 = pypywheels/manylinux2010-pypy_x86_64:2020-04-25-eb2cdff
 
 [aarch64]
-manylinux2014 = quay.io/pypa/manylinux2014_aarch64:2020-03-07-06139da
+manylinux2014 = quay.io/pypa/manylinux2014_aarch64:2020-05-01-b37d76b
 
 [ppc64le]
-manylinux2014 = quay.io/pypa/manylinux2014_ppc64le:2020-03-07-06139da
+manylinux2014 = quay.io/pypa/manylinux2014_ppc64le:2020-05-01-b37d76b
 
 [s390x]
-manylinux2014 = quay.io/pypa/manylinux2014_s390x:2020-03-07-06139da
+manylinux2014 = quay.io/pypa/manylinux2014_s390x:2020-05-01-b37d76b
 
diff --git a/cibuildwheel/resources/pypy3.6.patch b/cibuildwheel/resources/pypy3.6.patch
deleted file mode 100644
index b42d4bfd..00000000
--- a/cibuildwheel/resources/pypy3.6.patch
+++ /dev/null
@@ -1,7 +0,0 @@
---- 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 e6f14ed9..a389fac9 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -36,19 +36,19 @@ def get_python_configurations(build_selector):
     PythonConfiguration = namedtuple('PythonConfiguration', ['version', 'arch', 'identifier', 'url'])
     python_configurations = [
         # CPython
-        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='2.7.18', arch='32', identifier='cp27-win32', url=None),
+        PythonConfiguration(version='2.7.18', 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='3.7.7', arch='32', identifier='cp37-win32', url=None),
+        PythonConfiguration(version='3.7.7', arch='64', identifier='cp37-win_amd64', url=None),
         PythonConfiguration(version='3.8.2', arch='32', identifier='cp38-win32', url=None),
         PythonConfiguration(version='3.8.2', arch='64', identifier='cp38-win_amd64', url=None),
         # PyPy
-        PythonConfiguration(version='2.7', arch='32', identifier='pp27-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy2.7-v7.3.0-win32.zip'),
-        PythonConfiguration(version='3.6', arch='32', identifier='pp36-win32', url='https://bitbucket.org/pypy/pypy/downloads/pypy3.6-v7.3.0-win32.zip'),
+        PythonConfiguration(version='2.7', arch='32', identifier='pp27-win32', url='https://downloads.python.org/pypy/pypy2.7-v7.3.1-win32.zip'),
+        PythonConfiguration(version='3.6', arch='32', identifier='pp36-win32', url='https://downloads.python.org/pypy/pypy3.6-v7.3.1-win32.zip'),
     ]
 
     if IS_RUNNING_ON_TRAVIS:
@@ -86,7 +86,6 @@ def install_pypy(version, arch, url):
         extract_zip(pypy_zip, os.path.dirname(installation_path))
         pypy_exe = 'pypy3.exe' if version[0] == '3' else 'pypy.exe'
         shell(['mklink', os.path.join(installation_path, 'python.exe'), os.path.join(installation_path, pypy_exe)])
-        shell(['mklink', '/d', os.path.join(installation_path, 'Scripts'), os.path.join(installation_path, 'bin')])
     return installation_path
 
 
@@ -199,9 +198,6 @@ def build(options: BuildOptions):
             virtualenv_env = env.copy()
 
             venv_script_path = os.path.join(venv_dir, 'Scripts')
-            if os.path.exists(os.path.join(venv_dir, 'bin')):
-                # pypy2.7 bugfix
-                venv_script_path = os.pathsep.join([venv_script_path, os.path.join(venv_dir, 'bin')])
             virtualenv_env['PATH'] = os.pathsep.join([
                 venv_script_path,
                 virtualenv_env['PATH'],
diff --git a/docs/cpp_standards.md b/docs/cpp_standards.md
index 88ff6578..5dd83614 100644
--- a/docs/cpp_standards.md
+++ b/docs/cpp_standards.md
@@ -22,12 +22,22 @@ However, to enable modern C++ standards, the deploment target needs to be set hi
 
 To get C++11 and C++14 support, `MACOSX_DEPLOYMENT_TARGET` needs to be set to (at least) `"10.9"`. By default, `cibuildwheel` already does this, building 64-bit-only wheels for macOS 10.9 and later.
 
-To get C++17 support, set `MACOSX_DEPLOYMENT_TARGET` to (at least) `"10.13"` or `"10.14"` (macOS 10.13 offers partial C++17 support; e.g., the filesystem header is in experimental, offering `#include <experimental/filesystem>` instead of `#include <filesystem>`; macOS 10.14 has full C++17 support).
+To get C++17 support, Xcode 9.3+ is needed, requiring at least macOS 10.13 on the build machine. To use C++17 library features and link against the C++ runtime library, set `MACOSX_DEPLOYMENT_TARGET` to `"10.13"` or `"10.14"` (or higher) - macOS 10.13 offers partial C++17 support (e.g., the filesystem header is in experimental, offering `#include <experimental/filesystem>` instead of `#include <filesystem>`); macOS 10.14 has full C++17 support.
 
-For more details see https://en.cppreference.com/w/cpp/compiler_support and https://xcodereleases.com/: Xcode 10 needs macOS 10.13 and Xcode 11 needs macOS 10.14.
+However, if only C++17 compiler and standard template library (STL) features are used (not needing a C++17 runtime) it might be possible to set `MACOSX_DEPLOYMENT_TARGET` to a lower value, such as `"10.9"`. To find out if this is the case, try compiling and running with a lower `MACOSX_DEPLOYMENT_TARGET`: if C++17 features are used that require a more recent deployment target, building the wheel should fail.
+
+For more details see https://en.cppreference.com/w/cpp/compiler_support, https://en.wikipedia.org/wiki/Xcode, and https://xcodereleases.com/: Xcode 10 needs macOS 10.13 and Xcode 11 needs macOS 10.14.
 
 ## Windows and Python 2.7
 
-Visual C++ for Python 2.7 does not support modern standards of C++. When building on Appveyor, you will need to either use the "Visual Studio 2017" or "Visual Studio 2019" image, but Python 2.7 is not supported on these images - skip it by setting `CIBW_SKIP=cp27-win*`.
+Visual C++ for Python 2.7 does not support modern C++ standards (i.e., C++11 and later). When building on Appveyor, you will need to either use the "Visual Studio 2017" or "Visual Studio 2019" image, but Python 2.7 is not supported on these images - skip it by setting `CIBW_SKIP=cp27-win*`.
 
-There is an optional workaround for this, though: the pybind11 project argues and shows that it is [possible to compile Python 2.7 extension with a newer compiler](https://pybind11.readthedocs.io/en/stable/faq.html#working-with-ancient-visual-studio-2008-builds-on-windows) and has an example project showing how to do this: https://github.com/pybind/python_example. The main catch is that a user might need to install a newer "Microsoft Visual C++ Redistributable", since the newer C++ standard libraries are not included by default with the Python 2.7 installation.
+There is an optional workaround for this, though: the pybind11 project argues and shows that it is [possible to compile Python 2.7 extension with a newer compiler](https://pybind11.readthedocs.io/en/stable/faq.html#working-with-ancient-visual-studio-2008-builds-on-windows) and has an example project showing how to do this: https://github.com/pybind/python_example. The main catch is that a user might need to install [a newer "Microsoft Visual C++ Redistributable"](https://support.microsoft.com/en-us/help/2977003/the-latest-supported-visual-c-downloads), since the newer C++ standard library's binaries are not included by default with the Python 2.7 installation.
+
+Forcing `distutils` or `setuptools` to use a more recent version of MSVC that supports modern C++ can be done in the following way:
+
+1. Set the environment variables `DISTUTILS_USE_SDK=1` and `MSSdk=1`. These two environment variables will tell `distutils`/`setuptools` to not search and set up a build environment that uses Visual C++ for Python 2.7 (aka. MSVC 9).
+2. Set up the build Visual Studio build environment you want to use, making sure that e.g. `PATH` contains `cl`, `link`, etc.
+    - Usually, this can be done through `vcvarsall.bat x86` or `vcvarsall.bat x64`. The exact location of this file depends on the installation, but the default path for VS 2019 Community (e.g. used in AppVeyor's `Visual Studio 2019` image) is `C:\Program Files (x86)\Microsoft Visual Studio\2019\Community\VC\Auxiliary\Build\vcvarsall.bat`. **Note**: `vcvarsall.bat` changes the environment variables, so this cannot be run in a subprocess/subshell and consequently running `vsvarsall.bat` in `CIBW_BEFORE_BUILD` does not have any effect.
+    - In Azure Pipelines, [a `VSBuild` task is available](https://docs.microsoft.com/en-us/azure/devops/pipelines/tasks/build/visual-studio-build) and GitHub Actions has [an action `microsoft/setup-msbuild`](https://github.com/microsoft/setup-msbuild) that help setting up the Visual Studio environment.
+3. Next, call `cibuildwheel`. Unfortunately, MSVC has separate toolchains for compiling 32-bit and 64-bit, so you will need to run `cibuildwheel` twice: once with `CIBW_BUILD=*-win32` after setting up the `x86` build environment, and once with `CIBW_BUILD=*-win_amd64` in a `x64` enviroment (see previous step).
diff --git a/examples/appveyor-minimal.yml b/examples/appveyor-minimal.yml
index 3314fba6..3f89bce4 100644
--- a/examples/appveyor-minimal.yml
+++ b/examples/appveyor-minimal.yml
@@ -12,7 +12,7 @@ stack: python 3.7
 init:
 - cmd: set PATH=C:\Python37;C:\Python37\Scripts;%PATH%
 
-install: python -m pip install cibuildwheel==1.3.0
+install: python -m pip install cibuildwheel==1.4.1
 
 build_script: python -m cibuildwheel --output-dir wheelhouse
 
diff --git a/examples/azure-pipelines-minimal.yml b/examples/azure-pipelines-minimal.yml
index 98cf1471..fbbdebb4 100644
--- a/examples/azure-pipelines-minimal.yml
+++ b/examples/azure-pipelines-minimal.yml
@@ -5,7 +5,7 @@ jobs:
     - task: UsePythonVersion@0
     - bash: |
         python3 -m pip install --upgrade pip
-        pip3 install cibuildwheel==1.3.0
+        pip3 install cibuildwheel==1.4.1
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
@@ -16,7 +16,7 @@ jobs:
     - task: UsePythonVersion@0
     - bash: |
         python3 -m pip install --upgrade pip
-        pip3 install cibuildwheel==1.3.0
+        pip3 install cibuildwheel==1.4.1
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
@@ -29,7 +29,7 @@ jobs:
       displayName: Install Visual C++ for Python 2.7
     - bash: |
         python -m pip install --upgrade pip
-        pip install cibuildwheel==1.3.0
+        pip install cibuildwheel==1.4.1
         cibuildwheel --output-dir wheelhouse .
     - task: PublishBuildArtifacts@1
       inputs: {pathtoPublish: 'wheelhouse'}
diff --git a/examples/circleci-minimal.yml b/examples/circleci-minimal.yml
index 7748d362..6794221c 100644
--- a/examples/circleci-minimal.yml
+++ b/examples/circleci-minimal.yml
@@ -11,7 +11,7 @@ jobs:
       - run:
           name: Build the Linux wheels.
           command: |
-            pip3 install --user cibuildwheel==1.3.0
+            pip3 install --user cibuildwheel==1.4.1
             cibuildwheel --output-dir wheelhouse
       - store_artifacts:
           path: wheelhouse/
@@ -25,7 +25,7 @@ jobs:
       - run:
           name: Build the OS X wheels.
           command: |
-            pip3 install --user cibuildwheel==1.3.0
+            pip3 install --user cibuildwheel==1.4.1
             cibuildwheel --output-dir wheelhouse
       - store_artifacts:
           path: wheelhouse/
diff --git a/examples/github-minimal.yml b/examples/github-minimal.yml
index 30913057..988c2298 100644
--- a/examples/github-minimal.yml
+++ b/examples/github-minimal.yml
@@ -20,7 +20,7 @@ jobs:
 
     - name: Install cibuildwheel
       run: |
-        python -m pip install cibuildwheel==1.3.0
+        python -m pip install cibuildwheel==1.4.1
 
     - name: Install Visual C++ for Python 2.7
       if: startsWith(matrix.os, 'windows')
diff --git a/examples/travis-ci-deploy-only.yml b/examples/travis-ci-deploy-only.yml
index a27968fe..cad4f5a3 100644
--- a/examples/travis-ci-deploy-only.yml
+++ b/examples/travis-ci-deploy-only.yml
@@ -25,7 +25,7 @@ env:
     # Note: TWINE_PASSWORD is set to a PyPI API token in Travis settings
 
 install:
-  - python3 -m pip install cibuildwheel==1.3.0
+  - python3 -m pip install cibuildwheel==1.4.1
 
 script:
   # build the wheels, put them into './wheelhouse'
diff --git a/examples/travis-ci-minimal.yml b/examples/travis-ci-minimal.yml
index ede3d173..4fc41c49 100644
--- a/examples/travis-ci-minimal.yml
+++ b/examples/travis-ci-minimal.yml
@@ -26,7 +26,7 @@ jobs:
         - ln -s /c/Python38/python.exe /c/Python38/python3.exe
 
 install:
-  - python3 -m pip install cibuildwheel==1.3.0
+  - python3 -m pip install cibuildwheel==1.4.1
 
 script:
   # build the wheels, put them into './wheelhouse'
diff --git a/examples/travis-ci-test-and-deploy.yml b/examples/travis-ci-test-and-deploy.yml
index e20d2fad..eada75c8 100644
--- a/examples/travis-ci-test-and-deploy.yml
+++ b/examples/travis-ci-test-and-deploy.yml
@@ -55,7 +55,7 @@ jobs:
     - stage: deploy
       name: Build and deploy Linux wheels
       services: docker
-      install: python3 -m pip install cibuildwheel==1.3.0
+      install: python3 -m pip install cibuildwheel==1.4.1
       script: python3 -m cibuildwheel --output-dir wheelhouse
       after_success: |
         python3 -m pip install twine
@@ -65,7 +65,7 @@ jobs:
       name: Build and deploy macOS wheels
       os: osx
       language: shell
-      install: python3 -m pip install cibuildwheel==1.3.0
+      install: python3 -m pip install cibuildwheel==1.4.1
       script: python3 -m cibuildwheel --output-dir wheelhouse
       after_success: |
         python3 -m pip install twine
@@ -75,7 +75,7 @@ jobs:
       name: Build and deploy Windows wheels
       os: windows
       language: shell
-      install: python3 -m pip install cibuildwheel==1.3.0
+      install: python3 -m pip install cibuildwheel==1.4.1
       script: python3 -m cibuildwheel --output-dir wheelhouse
       after_success: |
         python3 -m pip install twine
diff --git a/mkdocs.yml b/mkdocs.yml
index 5c12f501..4a10a6d9 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -28,6 +28,8 @@ markdown_extensions:
       permalink: True
   - attr_list
   - admonition
+  - pymdownx.magiclink:
+      repo_url_shortener: True
 
 plugins:
   - importmarkdown
diff --git a/requirements-dev.txt b/requirements-dev.txt
index f838e3f2..44043506 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -2,6 +2,7 @@
 -e ./docs/mkdocs_include_markdown_plugin
 pytest
 mkdocs==1.0.4
+pymdown-extensions
 pip-tools
 requests
 click
diff --git a/setup.py b/setup.py
index 4c721135..143e313c 100644
--- a/setup.py
+++ b/setup.py
@@ -13,7 +13,7 @@ with io.open(os.path.join(this_directory, 'README.md'), encoding='utf-8') as f:
 
 setup(
     name='cibuildwheel',
-    version='1.3.0',
+    version='1.4.1',
     install_requires=['bashlex!=0.13'],
     description="Build Python wheels on CI with minimal configuration.",
     long_description=long_description,
diff --git a/test/test_cpp_standards.py b/test/test_cpp_standards.py
index 3cc18917..5c73a9bc 100644
--- a/test/test_cpp_standards.py
+++ b/test/test_cpp_standards.py
@@ -105,14 +105,12 @@ def test_cpp14(tmp_path):
 
     # 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
-    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32 cp35-win*'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32'}
 
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
     expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0')
                        if 'cp27-cp27m-win' not in w
-                       and 'pp27-pypy_73-win32' not in w
-                       and 'cp35-cp35m-win' not in w]
+                       and 'pp27-pypy_73-win32' not in w]
 
     assert set(actual_wheels) == set(expected_wheels)
 
@@ -139,7 +137,7 @@ def test_cpp17(tmp_path):
     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* pp27-win32 cp35-win* pp36-win32'}
+    add_env = {'CIBW_SKIP': 'cp27-win* pp27-win32'}
 
     if utils.platform == 'macos':
         add_env['MACOSX_DEPLOYMENT_TARGET'] = '10.13'
@@ -147,8 +145,56 @@ def test_cpp17(tmp_path):
     actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env)
     expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0', macosx_deployment_target='10.13')
                        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]
+                       and 'pp27-pypy_73-win32' not in w]
+
+    assert set(actual_wheels) == set(expected_wheels)
+
+
+def test_cpp17_py27_modern_msvc_workaround():
+    # This test checks the workaround for building Python 2.7 wheel with MSVC 14
+
+    if utils.platform != 'windows':
+        pytest.skip('the test is only relevant to the Windows build')
+
+    if os.environ.get('APPVEYOR_BUILD_WORKER_IMAGE', '') == 'Visual Studio 2015':
+        pytest.skip('Visual Studio 2015 does not support C++17')
+
+    # VC++ for Python 2.7 (i.e., MSVC 9) does not support modern standards
+    # This is a workaround which forces distutils/setupstools to a newer version
+    # Wheels compiled need a more modern C++ redistributable installed, which is not
+    # included with Python: see documentation for more info
+    # DISTUTILS_USE_SDK and MSSdk=1 tell distutils/setuptools that we are adding
+    # MSVC's compiler, tools, and libraries to PATH ourselves
+    add_env = {'CIBW_ENVIRONMENT': 'STANDARD=17',
+               'DISTUTILS_USE_SDK': '1', 'MSSdk': '1'}
+
+    # Use existing setuptools code to run Visual Studio's vcvarsall.bat and get the
+    # necessary environment variables, since running vcvarsall.bat in a subprocess
+    # does not keep the relevant environment variables
+    # There are different environment variables for 32-bit/64-bit targets, so we
+    # need to run cibuildwheel twice, once for 32-bit with `vcvarsall.bat x86, and
+    # once for 64-bit with `vcvarsall.bat x64`
+    # In a normal CI setup, just run vcvarsall.bat before running cibuildwheel and set
+    # DISTUTILS_USE_SDK and MSSdk
+    import setuptools
+
+    def add_vcvars(prev_env, platform):
+        vcvarsall_env = setuptools.msvc.msvc14_get_vc_env(platform)
+        env = prev_env.copy()
+        for vcvar in ['path', 'include', 'lib']:
+            env[vcvar] = vcvarsall_env[vcvar]
+        return env
+
+    add_env_x86 = add_vcvars(add_env, 'x86')
+    add_env_x86['CIBW_BUILD'] = '?p27-win32'
+    actual_wheels = utils.cibuildwheel_run(project_dir, add_env=add_env_x86)
+
+    add_env_x64 = add_vcvars(add_env, 'x64')
+    add_env_x64['CIBW_BUILD'] = 'cp27-win_amd64'
+    actual_wheels += utils.cibuildwheel_run(project_dir, add_env=add_env_x64)
+
+    expected_wheels = [w for w in utils.expected_wheels('spam', '0.1.0')
+                       if 'cp27-cp27m-win' in w
+                       or 'pp27-pypy_73-win32' in w]
 
     assert set(actual_wheels) == set(expected_wheels)
diff --git a/test/test_testing.py b/test/test_testing.py
index ed60fded..64ad4bac 100644
--- a/test/test_testing.py
+++ b/test/test_testing.py
@@ -15,13 +15,52 @@ project_with_a_test = CTemplateProject(
 )
 
 project_with_a_test.files['test/spam_test.py'] = r'''
+import os
+import platform
+import sys
+import struct
 from unittest import TestCase
+
 import spam
 
+
+def path_contains(parent, child):
+    """ returns True if `child` is inside `parent`.
+    Works around path-comparison bugs caused by short-paths on Windows e.g.
+    vssadm~1 instead of vssadministrator
+    """
+    parent = os.path.abspath(parent)
+    child = os.path.abspath(child)
+
+    while child != os.path.dirname(child):
+        child = os.path.dirname(child)
+        if os.stat(parent) == os.stat(child):
+            # parent and child refer to the same directory on the filesystem
+            return True
+    return False
+
+
 class TestSpam(TestCase):
     def test_system(self):
         self.assertEqual(0, spam.system('python -c "exit(0)"'))
         self.assertNotEqual(0, spam.system('python -c "exit(1)"'))
+
+    def test_virtualenv(self):
+        virtualenv_path = os.environ.get("__CIBW_VIRTUALENV_PATH__")
+        if not virtualenv_path:
+            self.fail("No virtualenv path defined in environment variable __CIBW_VIRTUALENV_PATH__")
+
+        self.assertTrue(path_contains(virtualenv_path, sys.executable))
+        self.assertTrue(path_contains(virtualenv_path, spam.__file__))
+
+    def test_uname(self):
+        if platform.system() == "Windows":
+            return
+        # if we're running in 32-bit Python, check that the machine is i686.
+        # See #336 for more info.
+        bits = struct.calcsize("P") * 8
+        if bits == 32:
+            self.assertEqual(platform.machine(), "i686")
 '''