diff --git a/.clang-tidy b/.clang-tidy
index d01ca352c..e82443c4c 100644
--- a/.clang-tidy
+++ b/.clang-tidy
@@ -25,11 +25,12 @@ modernize-replace-random-shuffle,
 modernize-shrink-to-fit,
 modernize-use-auto,
 modernize-use-bool-literals,
+modernize-use-default-member-init,
 modernize-use-equals-default,
 modernize-use-equals-delete,
-modernize-use-default-member-init,
-modernize-use-noexcept,
 modernize-use-emplace,
+modernize-use-noexcept,
+modernize-use-nullptr,
 modernize-use-override,
 modernize-use-using,
 *performance*,
diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index d06ddfa11..335b78ff1 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -263,7 +263,7 @@ private:
     static npy_api lookup() {
         module_ m = module_::import("numpy.core.multiarray");
         auto c = m.attr("_ARRAY_API");
-        void **api_ptr = (void **) PyCapsule_GetPointer(c.ptr(), NULL);
+        void **api_ptr = (void **) PyCapsule_GetPointer(c.ptr(), nullptr);
         npy_api api;
 #define DECL_NPY_API(Func) api.Func##_ = (decltype(api.Func##_)) api_ptr[API_##Func];
         DECL_NPY_API(PyArray_GetNDArrayCFeatureVersion);
@@ -1549,7 +1549,7 @@ public:
     void *data() const { return p_ptr; }
 
 private:
-    char *p_ptr{0};
+    char *p_ptr{nullptr};
     container_type m_strides;
 };
 
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 97275e40a..ce05b6e4e 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -2489,7 +2489,7 @@ public:
     exception(handle scope, const char *name, handle base = PyExc_Exception) {
         std::string full_name
             = scope.attr("__name__").cast<std::string>() + std::string(".") + name;
-        m_ptr = PyErr_NewException(const_cast<char *>(full_name.c_str()), base.ptr(), NULL);
+        m_ptr = PyErr_NewException(const_cast<char *>(full_name.c_str()), base.ptr(), nullptr);
         if (hasattr(scope, "__dict__") && scope.attr("__dict__").contains(name)) {
             pybind11_fail("Error during initialization: multiple incompatible "
                           "definitions with name \""
diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 7d52774c8..26d9025c5 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -600,13 +600,13 @@ inline handle get_function(handle value) {
 inline PyObject *dict_getitemstring(PyObject *v, const char *key) {
     PyObject *kv = nullptr, *rv = nullptr;
     kv = PyUnicode_FromString(key);
-    if (kv == NULL) {
+    if (kv == nullptr) {
         throw error_already_set();
     }
 
     rv = PyDict_GetItemWithError(v, kv);
     Py_DECREF(kv);
-    if (rv == NULL && PyErr_Occurred()) {
+    if (rv == nullptr && PyErr_Occurred()) {
         throw error_already_set();
     }
     return rv;
@@ -614,7 +614,7 @@ inline PyObject *dict_getitemstring(PyObject *v, const char *key) {
 
 inline PyObject *dict_getitem(PyObject *v, PyObject *key) {
     PyObject *rv = PyDict_GetItemWithError(v, key);
-    if (rv == NULL && PyErr_Occurred()) {
+    if (rv == nullptr && PyErr_Occurred()) {
         throw error_already_set();
     }
     return rv;
diff --git a/tests/cross_module_gil_utils.cpp b/tests/cross_module_gil_utils.cpp
index 2e64da052..1436c35d6 100644
--- a/tests/cross_module_gil_utils.cpp
+++ b/tests/cross_module_gil_utils.cpp
@@ -25,8 +25,8 @@ void gil_acquire() { py::gil_scoped_acquire gil; }
 
 constexpr char kModuleName[] = "cross_module_gil_utils";
 
-struct PyModuleDef moduledef
-    = {PyModuleDef_HEAD_INIT, kModuleName, NULL, 0, NULL, NULL, NULL, NULL, NULL};
+struct PyModuleDef moduledef = {
+    PyModuleDef_HEAD_INIT, kModuleName, nullptr, 0, nullptr, nullptr, nullptr, nullptr, nullptr};
 
 } // namespace
 
@@ -34,7 +34,7 @@ extern "C" PYBIND11_EXPORT PyObject *PyInit_cross_module_gil_utils() {
 
     PyObject *m = PyModule_Create(&moduledef);
 
-    if (m != NULL) {
+    if (m != nullptr) {
         static_assert(sizeof(&gil_acquire) == sizeof(void *),
                       "Function pointer must have the same size as void*");
         PyModule_AddObject(
diff --git a/tests/test_numpy_dtypes.cpp b/tests/test_numpy_dtypes.cpp
index 7de36f2fe..38f2afa07 100644
--- a/tests/test_numpy_dtypes.cpp
+++ b/tests/test_numpy_dtypes.cpp
@@ -289,8 +289,8 @@ py::list test_dtype_ctors() {
     dict["itemsize"] = py::int_(20);
     list.append(py::dtype::from_args(dict));
     list.append(py::dtype(names, formats, offsets, 20));
-    list.append(py::dtype(py::buffer_info((void *) 0, sizeof(unsigned int), "I", 1)));
-    list.append(py::dtype(py::buffer_info((void *) 0, 0, "T{i:a:f:b:}", 1)));
+    list.append(py::dtype(py::buffer_info((void *) nullptr, sizeof(unsigned int), "I", 1)));
+    list.append(py::dtype(py::buffer_info((void *) nullptr, 0, "T{i:a:f:b:}", 1)));
     list.append(py::dtype(py::detail::npy_api::NPY_DOUBLE_));
     return list;
 }