diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
new file mode 100644
index 0000000000..a2627c7972
--- /dev/null
+++ b/.github/workflows/ci.yml
@@ -0,0 +1,81 @@
+name: CI
+
+on:
+  workflow_dispatch:
+  pull_request:
+  push:
+    branches:
+      - master
+      - stable
+      - v*
+
+jobs:
+  standard:
+    strategy:
+      fail-fast: false
+      matrix:
+        os: [ubuntu, windows, macos]
+        python:
+        - 2.7
+        - 3.5
+        - 3.8
+        - 3.9-dev
+        - pypy2
+        - pypy3
+
+        include:
+          - os: ubuntu
+            python: 3.6
+          - os: macos
+            python: 3.7
+
+        exclude:
+            # Currently 32bit only, and we build 64bit
+          - os: windows
+            python: pypy2
+          - os: windows
+            python: pypy3
+
+            # Currently can't build due to warning, fixed in CPython > 3.9b5
+          - os: macos
+            python: 3.9-dev
+
+            # Currently broken on embed_test
+          - os: windows
+            python: 3.8
+          - os: windows
+            python: 3.9-dev
+
+    name: Python ${{ matrix.python }} on ${{ matrix.os }}
+    runs-on: ${{ matrix.os }}-latest
+
+    steps:
+    - uses: actions/checkout@v2
+
+    - name: Setup Python ${{ matrix.python }}
+      uses: actions/setup-python@v2
+      with:
+        python-version: ${{ matrix.python }}
+
+    - name: Prepare env
+      run: python -m pip install -r tests/requirements.txt
+
+    - name: Configure
+      shell: bash
+      run: >
+        cmake -S . -B build
+        -DPYBIND11_WERROR=ON
+        -DDOWNLOAD_CATCH=ON
+        -DPYTHON_EXECUTABLE=$(python -c "import sys; print(sys.executable)")
+
+    - name: Build
+      run: cmake --build build -j 2
+
+    - name: Python tests
+      run: cmake --build build --target pytest -j 2 -v
+
+    - name: C++ tests
+      run: cmake --build build --target cpptest -j 2 -v
+
+    - name: Interface test
+      run: cmake --build build --target test_cmake_build
diff --git a/.gitignore b/.gitignore
index 244bbcaa7a..4dca42ab7e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -37,3 +37,4 @@ MANIFEST
 sosize-*.txt
 pybind11Config*.cmake
 pybind11Targets.cmake
+/*env*
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index e4aba75674..b1c72b76ac 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -151,6 +151,14 @@ function(pybind11_enable_warnings target_name)
       target_compile_options(${target_name} PRIVATE -Werror)
     endif()
   endif()
+
+  if(CMAKE_CXX_COMPILER_ID MATCHES "Clang" AND PYTHON_VERSION VERSION_LESS 3.0)
+    if(CMAKE_CXX_STANDARD STREQUAL "14")
+      target_compile_options(${target_name} PUBLIC -Wno-deprecated-register)
+    elseif(NOT CMAKE_CXX_STANDARD VERSION_LESS 17)
+      target_compile_options(${target_name} PUBLIC -Wno-register)
+    endif()
+  endif()
 endfunction()
 
 set(test_targets pybind11_tests)
@@ -203,10 +211,10 @@ foreach(target ${test_targets})
 
   # Always write the output file directly into the 'tests' directory (even on MSVC)
   if(NOT CMAKE_LIBRARY_OUTPUT_DIRECTORY)
-    set_target_properties(${target} PROPERTIES LIBRARY_OUTPUT_DIRECTORY ${testdir})
+    set_target_properties(${target} PROPERTIES LIBRARY_OUTPUT_DIRECTORY "${testdir}")
     foreach(config ${CMAKE_CONFIGURATION_TYPES})
       string(TOUPPER ${config} config)
-      set_target_properties(${target} PROPERTIES LIBRARY_OUTPUT_DIRECTORY_${config} ${testdir})
+      set_target_properties(${target} PROPERTIES LIBRARY_OUTPUT_DIRECTORY_${config} "${testdir}")
     endforeach()
   endif()
 endforeach()
diff --git a/tests/requirements.txt b/tests/requirements.txt
new file mode 100644
index 0000000000..37e06ca8df
--- /dev/null
+++ b/tests/requirements.txt
@@ -0,0 +1,3 @@
+--extra-index-url https://antocuni.github.io/pypy-wheels/manylinux2010/
+numpy; platform_python_implementation!="PyPy" or sys_platform!="darwin" or python_version<"3.0"
+pytest
diff --git a/tests/test_cmake_build/CMakeLists.txt b/tests/test_cmake_build/CMakeLists.txt
index c9b5fcb2e7..cf9a9ca9ff 100644
--- a/tests/test_cmake_build/CMakeLists.txt
+++ b/tests/test_cmake_build/CMakeLists.txt
@@ -13,6 +13,7 @@ function(pybind11_add_build_test name)
   set(build_options "-DCMAKE_PREFIX_PATH=${PROJECT_BINARY_DIR}/mock_install"
                     "-DCMAKE_CXX_COMPILER=${CMAKE_CXX_COMPILER}"
                     "-DPYTHON_EXECUTABLE:FILEPATH=${PYTHON_EXECUTABLE}"
+                    "-DCMAKE_CXX_STANDARD=${CMAKE_CXX_STANDARD}"
                     "-DPYBIND11_CPP_STANDARD=${PYBIND11_CPP_STANDARD}")
   if(NOT ARG_INSTALL)
     list(APPEND build_options "-DPYBIND11_PROJECT_DIR=${PROJECT_SOURCE_DIR}")
diff --git a/tests/test_embed/CMakeLists.txt b/tests/test_embed/CMakeLists.txt
index 8b4f1f843e..c5aa7c6c5e 100644
--- a/tests/test_embed/CMakeLists.txt
+++ b/tests/test_embed/CMakeLists.txt
@@ -17,25 +17,29 @@ add_executable(test_embed
   catch.cpp
   test_interpreter.cpp
 )
-target_include_directories(test_embed PRIVATE ${CATCH_INCLUDE_DIR})
+target_include_directories(test_embed PRIVATE "${CATCH_INCLUDE_DIR}")
 pybind11_enable_warnings(test_embed)
 
 if(NOT CMAKE_VERSION VERSION_LESS 3.0)
   target_link_libraries(test_embed PRIVATE pybind11::embed)
 else()
-  target_include_directories(test_embed PRIVATE ${PYBIND11_INCLUDE_DIR} ${PYTHON_INCLUDE_DIRS})
-  target_compile_options(test_embed PRIVATE ${PYBIND11_CPP_STANDARD})
-  target_link_libraries(test_embed PRIVATE ${PYTHON_LIBRARIES})
+  target_include_directories(test_embed PRIVATE "${PYBIND11_INCLUDE_DIR}" "${PYTHON_INCLUDE_DIRS}")
+  target_compile_options(test_embed PRIVATE "${PYBIND11_CPP_STANDARD}")
+  target_link_libraries(test_embed PRIVATE "${PYTHON_LIBRARIES}")
 endif()
 
 find_package(Threads REQUIRED)
 target_link_libraries(test_embed PUBLIC ${CMAKE_THREAD_LIBS_INIT})
 
 add_custom_target(cpptest COMMAND $<TARGET_FILE:test_embed>
-                  WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})
+                  WORKING_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}")
 
 pybind11_add_module(external_module THIN_LTO external_module.cpp)
-set_target_properties(external_module PROPERTIES LIBRARY_OUTPUT_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR})
+set_target_properties(external_module PROPERTIES LIBRARY_OUTPUT_DIRECTORY "${CMAKE_CURRENT_SOURCE_DIR}")
+foreach(config ${CMAKE_CONFIGURATION_TYPES})
+  string(TOUPPER ${config} config)
+  set_target_properties(external_module PROPERTIES LIBRARY_OUTPUT_DIRECTORY_${config} "${CMAKE_CURRENT_SOURCE_DIR}")
+endforeach()
 add_dependencies(cpptest external_module)
 
 add_dependencies(check cpptest)
diff --git a/tests/test_kwargs_and_defaults.py b/tests/test_kwargs_and_defaults.py
index 6c72a93689..531a9fdae7 100644
--- a/tests/test_kwargs_and_defaults.py
+++ b/tests/test_kwargs_and_defaults.py
@@ -2,6 +2,11 @@
 import pytest
 from pybind11_tests import kwargs_and_defaults as m
 
+import platform
+import sys
+
+pypy = platform.python_implementation() == "PyPy"
+
 
 def test_function_signatures(doc):
     assert doc(m.kw_func0) == "kw_func0(arg0: int, arg1: int) -> str"
@@ -146,6 +151,8 @@ def test_keyword_only_args(msg):
     """
 
 
+@pytest.mark.xfail(pypy and sys.version_info < (3, 0),
+                   reason="PyPy2 doesn't seem to double count")
 def test_args_refcount():
     """Issue/PR #1216 - py::args elements get double-inc_ref()ed when combined with regular
     arguments"""
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index 5d2ccf8fd1..4cfc707a32 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -322,7 +322,8 @@ def test_memoryview_from_buffer_empty_shape():
     assert view.format == 'B'
     if sys.version_info.major < 3:
         # Python 2 behavior is weird, but Python 3 (the future) is fine.
-        assert bytes(view).startswith(b'<memory at ')
+        # PyPy3 has <memoryview, while CPython 2 has <memory
+        assert bytes(view).startswith(b'<memory')
     else:
         assert bytes(view) == b''