diff --git a/.appveyor.yml b/.appveyor.yml
index c8205eae..ffcd7e3b 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -30,7 +30,7 @@ environment:
       PYTHON: C:\\Python36-x64
       PYTHON_VERSION: 3.6.x
       PYTHON_ARCH: 64
-      MSVC: 16.6.5
+      MSVC: 16.7.4
       ARCH: x86_64
       BOOST_PREFIX: C:\Libraries\boost_1_73_0
 
diff --git a/.travis.yml b/.travis.yml
index ef7828c6..657386bb 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -28,20 +28,26 @@ jobs:
       env: CXX=clang++ PYTHON=python3 CXXFLAGS=-std=c++98
     - os: linux
       env: CXX=clang++ PYTHON=python3 CXXFLAGS=-std=c++11
+    - os: linux
+      env: CXX=g++ PYTHON=pypy3 CXXFLAGS=-std=c++11
     - os: osx
       env: CXX=clang++ PYTHON=python CXXFLAGS=-std=c++11
     - env: PYTHON=python DOC=1
   allow_failures:
+    - os: linux
+      env: CXX=g++ PYTHON=pypy3 CXXFLAGS=-std=c++11
     - os: osx
 
 addons:
   apt:
     sources:
     - ubuntu-toolchain-r-test
+    - pypy
     packages:
     - gcc
     - g++
     - clang
+    - pypy3-dev
     - python3-pip
     - python-numpy
     - python-sphinx
diff --git a/include/boost/python/call.hpp b/include/boost/python/call.hpp
index 5d2d7d23..c057ee9a 100644
--- a/include/boost/python/call.hpp
+++ b/include/boost/python/call.hpp
@@ -60,7 +60,7 @@ call(PyObject* callable
     )
 {
     PyObject* const result = 
-        PyEval_CallFunction(
+        PyObject_CallFunction(
             callable
             , const_cast<char*>("(" BOOST_PP_REPEAT_1ST(N, BOOST_PYTHON_FIXED, "O") ")")
             BOOST_PP_REPEAT_1ST(N, BOOST_PYTHON_FAST_ARG_TO_PYTHON_GET, nil)
@@ -69,7 +69,7 @@ call(PyObject* callable
     // This conversion *must not* be done in the same expression as
     // the call, because, in the special case where the result is a
     // reference a Python object which was created by converting a C++
-    // argument for passing to PyEval_CallFunction, its reference
+    // argument for passing to PyObject_CallFunction, its reference
     // count will be 2 until the end of the full expression containing
     // the conversion, and that interferes with dangling
     // pointer/reference detection.
diff --git a/include/boost/python/call_method.hpp b/include/boost/python/call_method.hpp
index 410f6682..424077ea 100644
--- a/include/boost/python/call_method.hpp
+++ b/include/boost/python/call_method.hpp
@@ -69,7 +69,7 @@ call_method(PyObject* self, char const* name
     // This conversion *must not* be done in the same expression as
     // the call, because, in the special case where the result is a
     // reference a Python object which was created by converting a C++
-    // argument for passing to PyEval_CallFunction, its reference
+    // argument for passing to PyObject_CallFunction, its reference
     // count will be 2 until the end of the full expression containing
     // the conversion, and that interferes with dangling
     // pointer/reference detection.
diff --git a/include/boost/python/override.hpp b/include/boost/python/override.hpp
index 39714257..b631226f 100644
--- a/include/boost/python/override.hpp
+++ b/include/boost/python/override.hpp
@@ -97,7 +97,7 @@ class override : public object
     operator()() const
     {
         detail::method_result x(
-            PyEval_CallFunction(
+            PyObject_CallFunction(
                 this->ptr()
               , const_cast<char*>("()")
             ));
@@ -132,7 +132,7 @@ detail::method_result
 operator()( BOOST_PP_ENUM_BINARY_PARAMS_Z(1, N, A, const& a) ) const
 {
     detail::method_result x(
-        PyEval_CallFunction(
+        PyObject_CallFunction(
             this->ptr()
           , const_cast<char*>("(" BOOST_PP_REPEAT_1ST(N, BOOST_PYTHON_FIXED, "O") ")")
             BOOST_PP_REPEAT_1ST(N, BOOST_PYTHON_fast_arg_to_python_get, nil)
diff --git a/src/exec.cpp b/src/exec.cpp
index 171c6f41..b2eabe59 100644
--- a/src/exec.cpp
+++ b/src/exec.cpp
@@ -104,14 +104,22 @@ object BOOST_PYTHON_DECL exec_file(char const *filename, object global, object l
   if (local.is_none()) local = global;
   // should be 'char const *' but older python versions don't use 'const' yet.
   char *f = const_cast<char *>(filename);
-  // Let python open the file to avoid potential binary incompatibilities.
-#if PY_VERSION_HEX >= 0x03040000
-  FILE *fs = _Py_fopen(f, "r");
-#elif PY_VERSION_HEX >= 0x03000000
+#if PY_VERSION_HEX >= 0x03010000
+  // Let python manage any UTF bits to avoid potential incompatibilities.
   PyObject *fo = Py_BuildValue("s", f);
-  FILE *fs = _Py_fopen(fo, "r");
+  PyObject *fb = Py_None;
+  PyUnicode_FSConverter(fo, &fb);
+  f = PyBytes_AsString(fb);
+  FILE *fs = fopen(f, "r");
+  Py_DECREF(fo);
+  Py_DECREF(fb);
+#elif PY_VERSION_HEX >= 0x03000000
+  // Let python open the file to avoid potential binary incompatibilities.
+  PyObject *fo = Py_BuildValue("s", f);
+  FILE *fs = _Py_fopen(fo, "r"); // Private CPython API
   Py_DECREF(fo);
 #else
+  // Let python open the file to avoid potential binary incompatibilities.
   PyObject *pyfile = PyFile_FromString(f, const_cast<char*>("r"));
   if (!pyfile) throw std::invalid_argument(std::string(f) + " : no such file");
   python::handle<> file(pyfile);
diff --git a/src/wrapper.cpp b/src/wrapper.cpp
index f8feaef9..8b1b8847 100644
--- a/src/wrapper.cpp
+++ b/src/wrapper.cpp
@@ -25,7 +25,7 @@ namespace detail
             
               if (
                   PyMethod_Check(m.get())
-                  && ((PyMethodObject*)m.get())->im_self == this->m_self
+                  && PyMethod_GET_SELF(m.get()) == this->m_self
                   && class_object->tp_dict != 0
               )
               {
@@ -34,7 +34,7 @@ namespace detail
 
 
               }
-              if (borrowed_f != ((PyMethodObject*)m.get())->im_func)
+              if (borrowed_f != PyMethod_GET_FUNCTION(m.get()))
                   return override(m);
           }
       }