diff --git a/README.rst b/README.rst
index 8c04ba61a..9dfac6d7b 100644
--- a/README.rst
+++ b/README.rst
@@ -146,7 +146,7 @@ Image content
 
 All images currently contain:
 
-- CPython 3.5, 3.6, 3.7, 3.8 and 3.9, installed in
+- CPython 3.6, 3.7, 3.8 and 3.9, PyPy 3.7 installed in
   ``/opt/python/<python tag>-<abi tag>``. The directories are named
   after the PEP 425 tags for each environment --
   e.g. ``/opt/python/cp37-cp37m`` contains a CPython 3.7 build, and
@@ -165,6 +165,8 @@ default ``sys.abiflags`` became an empty string: the ``m`` flag for pymalloc
 became useless (builds with and without pymalloc are ABI compatible) and so has
 been removed. (e.g. ``/opt/python/cp38-cp38``)
 
+Note that PyPy is not available on ppc64le & s390x.
+
 Building Docker images
 ----------------------
 
diff --git a/docker/Dockerfile b/docker/Dockerfile
index b48ef11fb..31aacdd4f 100644
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -131,7 +131,9 @@ COPY build_scripts/cpython-pubkey-310-311.txt /build_scripts/cpython-pubkeys.txt
 RUN manylinux-entrypoint /build_scripts/build-cpython.sh 3.10.0b1
 
 
-FROM build_cpython AS all_cpython
+FROM build_cpython AS all_python
+COPY build_scripts/install-pypy.sh /build_scripts/install-pypy.sh
+RUN manylinux-entrypoint /build_scripts/install-pypy.sh 3.7 7.3.4
 COPY --from=build_cpython36 /opt/_internal /opt/_internal/
 COPY --from=build_cpython37 /opt/_internal /opt/_internal/
 COPY --from=build_cpython38 /opt/_internal /opt/_internal/
@@ -144,7 +146,7 @@ FROM runtime_base
 COPY --from=build_git /manylinux-rootfs /
 COPY --from=build_swig /manylinux-rootfs /
 COPY --from=build_cpython /manylinux-rootfs /
-COPY --from=all_cpython /opt/_internal /opt/_internal/
+COPY --from=all_python /opt/_internal /opt/_internal/
 COPY build_scripts/finalize.sh build_scripts/update-system-packages.sh build_scripts/python-tag-abi-tag.py build_scripts/requirements.txt build_scripts/requirements-tools.txt /build_scripts/
 RUN manylinux-entrypoint /build_scripts/finalize.sh && rm -rf /build_scripts
 
diff --git a/docker/build_scripts/finalize.sh b/docker/build_scripts/finalize.sh
index d375e1327..103996619 100755
--- a/docker/build_scripts/finalize.sh
+++ b/docker/build_scripts/finalize.sh
@@ -10,7 +10,7 @@ MY_DIR=$(dirname "${BASH_SOURCE[0]}")
 source $MY_DIR/build_utils.sh
 
 mkdir /opt/python
-for PREFIX in $(find /opt/_internal/ -mindepth 1 -maxdepth 1 -name 'cpython*'); do
+for PREFIX in $(find /opt/_internal/ -mindepth 1 -maxdepth 1 \( -name 'cpython*' -o -name 'pypy*' \)); do
 	# Some python's install as bin/python3. Make them available as
 	# bin/python.
 	if [ -e ${PREFIX}/bin/python3 ] && [ ! -e ${PREFIX}/bin/python ]; then
@@ -28,8 +28,12 @@ for PREFIX in $(find /opt/_internal/ -mindepth 1 -maxdepth 1 -name 'cpython*');
 	ln -s ${PREFIX} /opt/python/${ABI_TAG}
 	# Make versioned python commands available directly in environment.
 	PYVERS=$(${PREFIX}/bin/python -c "import sys; print('.'.join(map(str, sys.version_info[:2])))")
-	ln -s ${PREFIX}/bin/python /usr/local/bin/python${PYVERS}
-	ln -s ${PREFIX}/bin/pip /usr/local/bin/pip${PYVERS}
+	if [[ "${PREFIX}" == *"/pypy"* ]]; then
+		ln -s ${PREFIX}/bin/python /usr/local/bin/pypy${PYVERS}
+	else
+		ln -s ${PREFIX}/bin/python /usr/local/bin/python${PYVERS}
+		ln -s ${PREFIX}/bin/pip /usr/local/bin/pip${PYVERS}
+	fi
 done
 
 # Create venv for auditwheel & certifi
diff --git a/docker/build_scripts/install-pypy.sh b/docker/build_scripts/install-pypy.sh
new file mode 100755
index 000000000..d820ca763
--- /dev/null
+++ b/docker/build_scripts/install-pypy.sh
@@ -0,0 +1,65 @@
+#!/bin/bash
+
+# Stop at any error, show all commands
+set -exuo pipefail
+
+# Get script directory
+MY_DIR=$(dirname "${BASH_SOURCE[0]}")
+
+# Get build utilities
+source $MY_DIR/build_utils.sh
+
+
+PYTHON_VERSION=$1
+PYPY_VERSION=$2
+PYPY_DOWNLOAD_URL=https://downloads.python.org/pypy
+
+
+function get_shortdir {
+	local exe=$1
+	$exe -c 'import sys; print("pypy%d.%d-%d.%d.%d" % (sys.version_info[:2]+sys.pypy_version_info[:3]))'
+}
+
+
+mkdir -p /tmp
+cd /tmp
+
+case ${AUDITWHEEL_ARCH} in
+	x86_64) PYPY_ARCH=linux64;;
+	i686) PYPY_ARCH=linux32;;
+	aarch64) PYPY_ARCH=aarch64;;
+	*) echo "No PyPy for ${AUDITWHEEL_ARCH}"; exit 0;;
+esac
+
+TARBALL=pypy${PYTHON_VERSION}-v${PYPY_VERSION}-${PYPY_ARCH}.tar.bz2
+TMPDIR=/tmp/${TARBALL/.tar.bz2//}
+PREFIX="/opt/_internal"
+
+mkdir -p ${PREFIX}
+
+fetch_source ${TARBALL} ${PYPY_DOWNLOAD_URL}
+
+tar -xf ${TARBALL}
+
+# the new PyPy 3 distributions don't have pypy symlinks to pypy3
+if [ ! -f "${TMPDIR}/bin/pypy" ]; then
+	ln -s pypy3 ${TMPDIR}/bin/pypy
+fi
+
+# rename the directory to something shorter like pypy3.7-7.3.4
+PREFIX=${PREFIX}/$(get_shortdir ${TMPDIR}/bin/pypy)
+mv ${TMPDIR} ${PREFIX}
+
+# add a generic "python" symlink
+if [ ! -f "${PREFIX}/bin/python" ]; then
+	ln -s pypy ${PREFIX}/bin/python
+fi
+
+# remove debug symbols
+rm ${PREFIX}/bin/*.debug
+
+# We do not need the Python test suites
+find ${PREFIX} -depth \( -type d -a -name test -o -name tests \) | xargs rm -rf
+
+# We do not need precompiled .pyc and .pyo files.
+clean_pyc ${PREFIX}
diff --git a/tests/run_tests.sh b/tests/run_tests.sh
index c945ecfbb..8ffd44e39 100755
--- a/tests/run_tests.sh
+++ b/tests/run_tests.sh
@@ -24,17 +24,24 @@ for PYTHON in /opt/python/*/bin/python; do
 	$PYTHON $MY_DIR/manylinux-check.py ${AUDITWHEEL_POLICY} ${AUDITWHEEL_ARCH}
 	# Make sure that SSL cert checking works
 	$PYTHON $MY_DIR/ssl-check.py
-	# Make sure sqlite3 module can be loaded properly and is the manylinux version one
-	# c.f. https://github.com/pypa/manylinux/issues/1030
-	$PYTHON -c 'import sqlite3; print(sqlite3.sqlite_version); assert sqlite3.sqlite_version_info[0:2] >= (3, 34)'
-	# pythonx.y & pipx.y shall be available directly in PATH
+	IMPLEMENTATION=$(${PYTHON} -c "import sys; print(sys.implementation.name)")
 	PYVERS=$(${PYTHON} -c "import sys; print('.'.join(map(str, sys.version_info[:2])))")
-	LINK_VERSION=$(python${PYVERS} -V)
+	if [ "${IMPLEMENTATION}" == "pypy" ]; then
+		LINK_PREFIX=pypy
+	else
+		LINK_PREFIX=python
+		# Make sure sqlite3 module can be loaded properly and is the manylinux version one
+		# c.f. https://github.com/pypa/manylinux/issues/1030
+		$PYTHON -c 'import sqlite3; print(sqlite3.sqlite_version); assert sqlite3.sqlite_version_info[0:2] >= (3, 34)'
+		# pipx.y shall be available directly in PATH
+		LINK_VERSION=$(pip${PYVERS} -V)
+		REAL_VERSION=$(${PYTHON} -m pip -V)
+		test "${LINK_VERSION%% from *}" = "${REAL_VERSION%% from *}"
+	fi
+	# pythonx.y or pypyx.y shall be available directly in PATH
+	LINK_VERSION=$(${LINK_PREFIX}${PYVERS} -V)
 	REAL_VERSION=$(${PYTHON} -V)
 	test "${LINK_VERSION}" = "${REAL_VERSION}"
-	LINK_VERSION=$(pip${PYVERS} -V)
-	REAL_VERSION=$(${PYTHON} -m pip -V)
-	test "${LINK_VERSION%% from *}" = "${REAL_VERSION%% from *}"
 done
 
 # minimal tests for tools that should be present