diff --git a/README.md b/README.md
index 51044638..062edf6b 100644
--- a/README.md
+++ b/README.md
@@ -23,8 +23,9 @@ What does it do?
 | CPython 3.7     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅² | ✅² | ✅³ |
 | CPython 3.8     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅² | ✅² | ✅³ |
 | CPython 3.9     | ✅ | ✅  | ✅  | ✅ | ✅ | ✅² | ✅² | ✅³ |
-| PyPy 2.7 v7.3.0 | ✅ |    | ✅  | ✅ |    |    |    |    |
-| PyPy 3.6 v7.3.0 | ✅ |    | ✅  | ✅ |    |    |    |    |
+| PyPy 2.7 v7.3.2 | ✅ |    | ✅  | ✅ |    |    |    |    |
+| PyPy 3.6 v7.3.2 | ✅ |    | ✅  | ✅ |    |    |    |    |
+| PyPy 3.7 (alpha) v7.3.2 | ✅ |    | ✅  | ✅ |    |    |    |    |
 
 <sup>¹ Not supported on Travis</sup><br>
 <sup>² Only supported on Travis</sup><br>
diff --git a/cibuildwheel/macos.py b/cibuildwheel/macos.py
index 0d07d32a..9383119b 100644
--- a/cibuildwheel/macos.py
+++ b/cibuildwheel/macos.py
@@ -40,8 +40,9 @@ def get_python_configurations(build_selector: BuildSelector) -> List[PythonConfi
         PythonConfiguration(version='3.8', identifier='cp38-macosx_x86_64', url='https://www.python.org/ftp/python/3.8.4/python-3.8.4-macosx10.9.pkg'),
         PythonConfiguration(version='3.9', identifier='cp39-macosx_x86_64', url='https://www.python.org/ftp/python/3.9.0/python-3.9.0rc1-macosx10.9.pkg'),
         # PyPy
-        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'),
+        PythonConfiguration(version='2.7', identifier='pp27-macosx_x86_64', url='https://downloads.python.org/pypy/pypy2.7-v7.3.2rc1-osx64.tar.bz2'),
+        PythonConfiguration(version='3.6', identifier='pp36-macosx_x86_64', url='https://downloads.python.org/pypy/pypy3.6-v7.3.2rc1-osx64.tar.bz2'),
+        PythonConfiguration(version='3.7', identifier='pp37-macosx_x86_64', url='https://downloads.python.org/pypy/pypy3.7-v7.3.2rc1-osx64.tar.bz2'),
     ]
 
     # skip builds as required
diff --git a/cibuildwheel/windows.py b/cibuildwheel/windows.py
index 9eb8c9e9..c21eb60a 100644
--- a/cibuildwheel/windows.py
+++ b/cibuildwheel/windows.py
@@ -61,8 +61,9 @@ def get_python_configurations(build_selector: BuildSelector) -> List[PythonConfi
         PythonConfiguration(version='3.9.0-rc1', arch='32', identifier='cp39-win32', url=None),
         PythonConfiguration(version='3.9.0-rc1', arch='64', identifier='cp39-win_amd64', url=None),
         # PyPy
-        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'),
+        PythonConfiguration(version='2.7', arch='32', identifier='pp27-win32', url='https://downloads.python.org/pypy/pypy2.7-v7.3.2rc1-win32.zip'),
+        PythonConfiguration(version='3.6', arch='32', identifier='pp36-win32', url='https://downloads.python.org/pypy/pypy3.6-v7.3.2rc1-win32.zip'),
+        PythonConfiguration(version='3.7', arch='32', identifier='pp37-win32', url='https://downloads.python.org/pypy/pypy3.7-v7.3.2rc1-win32.zip'),
     ]
 
     if IS_RUNNING_ON_TRAVIS:
diff --git a/docs/options.md b/docs/options.md
index 856f0bad..3d37f3e4 100644
--- a/docs/options.md
+++ b/docs/options.md
@@ -86,13 +86,15 @@ When setting the options, you can use shell-style globbing syntax (as per [`fnma
 | 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     |                        |                        |                      |
+| PyPy 2.7 v7.3.2 | pp27-macosx_x86_64  | pp27-manylinux_x86_64  |                      |                 | pp27-win32     |                        |                        |                      |
+| PyPy 3.6 v7.3.2 | pp36-macosx_x86_64  | pp36-manylinux_x86_64  |                      |                 | pp36-win32     |                        |                        |                      |
+| PyPy 3.7 (alpha) v7.3.2 | pp37-macosx_x86_64  | pp37-manylinux_x86_64  |                      |                 | pp37-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.
+For CPython, the minimally supported macOS version is 10.9; for PyPy 2.7 and PyPy 3.6/3.7, respectively macOS 10.7 and 10.13 or higher is required.
 
 #### Examples