diff --git a/include/fmt/core.h b/include/fmt/core.h
index bb56da7f..de6164fe 100644
--- a/include/fmt/core.h
+++ b/include/fmt/core.h
@@ -1146,6 +1146,9 @@ constexpr bool is_arithmetic_type(type t) {
 struct unformattable {};
 struct unformattable_char : unformattable {};
 struct unformattable_const : unformattable {};
+struct unformattable_function_pointer : unformattable {};
+struct unformattable_member_function_pointer : unformattable {};
+struct unformattable_member_object_pointer : unformattable {};
 struct unformattable_pointer : unformattable {};
 
 template <typename Char> struct string_value {
@@ -1228,6 +1231,9 @@ template <typename Context> class value {
   value(unformattable_char);
   value(unformattable_const);
   value(unformattable_pointer);
+  value(unformattable_function_pointer);
+  value(unformattable_member_function_pointer);
+  value(unformattable_member_object_pointer);
 
  private:
   // Formats an argument of a custom type, such as a user-defined class.
@@ -1368,11 +1374,32 @@ template <typename Context> struct arg_mapper {
     return val;
   }
 
+  template <typename T,
+            FMT_ENABLE_IF(std::is_function<typename std::remove_pointer<
+                              remove_cvref_t<T>>::type>::value)>
+  FMT_CONSTEXPR auto map(const T&) -> unformattable_function_pointer {
+    return {};
+  }
+
+  template <typename T, FMT_ENABLE_IF(std::is_member_object_pointer<T>::value)>
+  FMT_CONSTEXPR auto map(const T&) -> unformattable_member_object_pointer {
+    return {};
+  }
+
+  template <typename T,
+            FMT_ENABLE_IF(std::is_member_function_pointer<T>::value)>
+  FMT_CONSTEXPR auto map(const T&) -> unformattable_member_function_pointer {
+    return {};
+  }
+
   // We use SFINAE instead of a const T* parameter to avoid conflicting with
   // the C array overload.
+
   template <
       typename T,
-      FMT_ENABLE_IF(std::is_convertible<const T&, const void*>::value &&
+      FMT_ENABLE_IF(!std::is_function<typename std::remove_pointer<
+                        remove_cvref_t<T>>::type>::value &&
+                    std::is_convertible<const T&, const void*>::value &&
                     !std::is_convertible<const T&, const char_type*>::value)>
   FMT_CONSTEXPR auto map(const T&) -> unformattable_pointer {
     return {};
@@ -1677,6 +1704,27 @@ FMT_CONSTEXPR FMT_INLINE auto make_arg(T&& val) -> value<Context> {
   static_assert(formattable_pointer,
                 "Formatting of non-void pointers is disallowed.");
 
+  // Formatting of function pointers is disallowed.
+  constexpr bool formattable_function_pointer =
+      !std::is_same<decltype(arg),
+                    const unformattable_function_pointer&>::value;
+  static_assert(formattable_function_pointer,
+                "Formatting of function pointers is disallowed.");
+
+  // Formatting of member function pointers is disallowed.
+  constexpr bool formattable_member_function_pointer =
+      !std::is_same<decltype(arg),
+                    const unformattable_member_function_pointer&>::value;
+  static_assert(formattable_member_function_pointer,
+                "Formatting of member function pointers is disallowed.");
+
+  // Formatting of member object pointers is disallowed.
+  constexpr bool formattable_member_object_pointer =
+      !std::is_same<decltype(arg),
+                    const unformattable_member_object_pointer&>::value;
+  static_assert(formattable_member_object_pointer,
+                "Formatting of member object pointers is disallowed.");
+
   constexpr bool formattable =
       !std::is_same<decltype(arg), const unformattable&>::value;
   static_assert(
diff --git a/test/compile-error-test/CMakeLists.txt b/test/compile-error-test/CMakeLists.txt
index 8202f279..44bbb1ab 100644
--- a/test/compile-error-test/CMakeLists.txt
+++ b/test/compile-error-test/CMakeLists.txt
@@ -67,6 +67,12 @@ expect_compile_error("
   fmt::format(\"{}\", S());
 ")
 
+# Formatting a function
+expect_compile_error("
+  void (*f)();
+  fmt::format(\"{}\", f);
+")
+
 # Make sure that compiler features detected in the header
 # match the features detected in CMake.
 if (SUPPORTS_USER_DEFINED_LITERALS)
diff --git a/test/core-test.cc b/test/core-test.cc
index da3bc0f9..e1383e84 100644
--- a/test/core-test.cc
+++ b/test/core-test.cc
@@ -770,6 +770,13 @@ TEST(core_test, is_formattable) {
   static_assert(!fmt::is_formattable<unsigned char*, wchar_t>::value, "");
   static_assert(!fmt::is_formattable<const signed char*, wchar_t>::value, "");
   static_assert(!fmt::is_formattable<const unsigned char*, wchar_t>::value, "");
+
+  static_assert(!fmt::is_formattable<void (*)()>::value, "");
+
+  struct S;
+
+  static_assert(!fmt::is_formattable<int(S::*)>::value, "");
+  static_assert(!fmt::is_formattable<int (S::*)()>::value, "");
 }
 
 TEST(core_test, format) { EXPECT_EQ(fmt::format("{}", 42), "42"); }