diff --git a/include/pybind11/common.h b/include/pybind11/common.h
index 712c1a5d..dcb58107 100644
--- a/include/pybind11/common.h
+++ b/include/pybind11/common.h
@@ -179,6 +179,17 @@ extern "C" {
     }                                                                          \
     PyObject *pybind11_init()
 
+// Function return value and argument type deduction support.  When compiling under C++17 these
+// differ as C++17 makes the noexcept specifier part of the function type, while it is not part of
+// the type under earlier standards.
+#ifdef __cpp_noexcept_function_type
+#  define PYBIND11_NOEXCEPT_TPL_ARG , bool NoExceptions
+#  define PYBIND11_NOEXCEPT_SPECIFIER noexcept(NoExceptions)
+#else
+#  define PYBIND11_NOEXCEPT_TPL_ARG
+#  define PYBIND11_NOEXCEPT_SPECIFIER
+#endif
+
 NAMESPACE_BEGIN(pybind11)
 
 using ssize_t = Py_ssize_t;
@@ -564,16 +575,16 @@ struct nodelete { template <typename T> void operator()(T*) { } };
 NAMESPACE_BEGIN(detail)
 template <typename... Args>
 struct overload_cast_impl {
-    template <typename Return>
-    constexpr auto operator()(Return (*pf)(Args...)) const noexcept
+    template <typename Return /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    constexpr auto operator()(Return (*pf)(Args...) PYBIND11_NOEXCEPT_SPECIFIER) const noexcept
                               -> decltype(pf) { return pf; }
 
-    template <typename Return, typename Class>
-    constexpr auto operator()(Return (Class::*pmf)(Args...), std::false_type = {}) const noexcept
+    template <typename Return, typename Class /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    constexpr auto operator()(Return (Class::*pmf)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, std::false_type = {}) const noexcept
                               -> decltype(pmf) { return pmf; }
 
-    template <typename Return, typename Class>
-    constexpr auto operator()(Return (Class::*pmf)(Args...) const, std::true_type) const noexcept
+    template <typename Return, typename Class /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    constexpr auto operator()(Return (Class::*pmf)(Args...) const PYBIND11_NOEXCEPT_SPECIFIER, std::true_type) const noexcept
                               -> decltype(pmf) { return pmf; }
 };
 NAMESPACE_END(detail)
diff --git a/include/pybind11/functional.h b/include/pybind11/functional.h
index f1b0ebbb..7f1ffc1d 100644
--- a/include/pybind11/functional.h
+++ b/include/pybind11/functional.h
@@ -15,9 +15,12 @@
 NAMESPACE_BEGIN(pybind11)
 NAMESPACE_BEGIN(detail)
 
-template <typename Return, typename... Args> struct type_caster<std::function<Return(Args...)>> {
-    typedef std::function<Return(Args...)> type;
-    typedef typename std::conditional<std::is_same<Return, void>::value, void_type, Return>::type retval_type;
+template <typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+struct type_caster<std::function<Return(Args...) PYBIND11_NOEXCEPT_SPECIFIER>> {
+    using type = std::function<Return(Args...) PYBIND11_NOEXCEPT_SPECIFIER>;
+    using retval_type = conditional_t<std::is_same<Return, void>::value, void_type, Return>;
+    using function_type = Return (*) (Args...) PYBIND11_NOEXCEPT_SPECIFIER;
+
 public:
     bool load(handle src_, bool) {
         if (src_.is_none())
@@ -38,10 +41,9 @@ public:
         if (PyCFunction_Check(src_.ptr())) {
             auto c = reinterpret_borrow<capsule>(PyCFunction_GetSelf(src_.ptr()));
             auto rec = (function_record *) c;
-            using FunctionType = Return (*) (Args...);
 
-            if (rec && rec->is_stateless && rec->data[1] == &typeid(FunctionType)) {
-                struct capture { FunctionType f; };
+            if (rec && rec->is_stateless && rec->data[1] == &typeid(function_type)) {
+                struct capture { function_type f; };
                 value = ((capture *) &rec->data)->f;
                 return true;
             }
@@ -62,7 +64,7 @@ public:
         if (!f_)
             return none().inc_ref();
 
-        auto result = f_.template target<Return (*)(Args...)>();
+        auto result = f_.template target<function_type>();
         if (result)
             return cpp_function(*result, policy).release();
         else
diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index e6f4efdf..7d46f107 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1145,13 +1145,15 @@ template <typename T, int Flags> struct handle_type_name<array_t<T, Flags>> {
 
 NAMESPACE_END(detail)
 
-template <typename Func, typename Return, typename... Args>
-detail::vectorize_helper<Func, Return, Args...> vectorize(const Func &f, Return (*) (Args ...)) {
+template <typename Func, typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+detail::vectorize_helper<Func, Return, Args...>
+vectorize(const Func &f, Return (*) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER) {
     return detail::vectorize_helper<Func, Return, Args...>(f);
 }
 
-template <typename Return, typename... Args>
-detail::vectorize_helper<Return (*) (Args ...), Return, Args...> vectorize(Return (*f) (Args ...)) {
+template <typename Return, typename... Args /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+detail::vectorize_helper<Return (*) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER, Return, Args...>
+vectorize(Return (*f) (Args ...) PYBIND11_NOEXCEPT_SPECIFIER) {
     return vectorize<Return (*) (Args ...), Return, Args...>(f, f);
 }
 
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 6c884a86..1492cd29 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -44,8 +44,8 @@ public:
     cpp_function() { }
 
     /// Construct a cpp_function from a vanilla function pointer
-    template <typename Return, typename... Args, typename... Extra>
-    cpp_function(Return (*f)(Args...), const Extra&... extra) {
+    template <typename Return, typename... Args, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    cpp_function(Return (*f)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
         initialize(f, f, extra...);
     }
 
@@ -57,17 +57,17 @@ public:
     }
 
     /// Construct a cpp_function from a class method (non-const)
-    template <typename Return, typename Class, typename... Arg, typename... Extra>
-    cpp_function(Return (Class::*f)(Arg...), const Extra&... extra) {
+    template <typename Return, typename Class, typename... Arg, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    cpp_function(Return (Class::*f)(Arg...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
         initialize([f](Class *c, Arg... args) -> Return { return (c->*f)(args...); },
-                   (Return (*) (Class *, Arg...)) nullptr, extra...);
+                   (Return (*) (Class *, Arg...) PYBIND11_NOEXCEPT_SPECIFIER) nullptr, extra...);
     }
 
     /// Construct a cpp_function from a class method (const)
-    template <typename Return, typename Class, typename... Arg, typename... Extra>
-    cpp_function(Return (Class::*f)(Arg...) const, const Extra&... extra) {
+    template <typename Return, typename Class, typename... Arg, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    cpp_function(Return (Class::*f)(Arg...) const PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
         initialize([f](const Class *c, Arg... args) -> Return { return (c->*f)(args...); },
-                   (Return (*)(const Class *, Arg ...)) nullptr, extra...);
+                   (Return (*)(const Class *, Arg ...) PYBIND11_NOEXCEPT_SPECIFIER) nullptr, extra...);
     }
 
     /// Return the function name
@@ -80,8 +80,8 @@ protected:
     }
 
     /// Special internal constructor for functors, lambda functions, etc.
-    template <typename Func, typename Return, typename... Args, typename... Extra>
-    void initialize(Func &&f, Return (*)(Args...), const Extra&... extra) {
+    template <typename Func, typename Return, typename... Args, typename... Extra /*,*/ PYBIND11_NOEXCEPT_TPL_ARG>
+    void initialize(Func &&f, Return (*)(Args...) PYBIND11_NOEXCEPT_SPECIFIER, const Extra&... extra) {
         static_assert(detail::expected_num_args<Extra...>(sizeof...(Args)),
                       "The number of named arguments does not match the function signature");
 
@@ -160,7 +160,7 @@ protected:
         if (cast_in::has_kwargs) rec->has_kwargs = true;
 
         /* Stash some additional information used by an important optimization in 'functional.h' */
-        using FunctionType = Return (*)(Args...);
+        using FunctionType = Return (*)(Args...) PYBIND11_NOEXCEPT_SPECIFIER;
         constexpr bool is_function_ptr =
             std::is_convertible<Func, FunctionType>::value &&
             sizeof(capture) == sizeof(void *);
diff --git a/tests/test_constants_and_functions.cpp b/tests/test_constants_and_functions.cpp
index c8c0392c..653bdf6b 100644
--- a/tests/test_constants_and_functions.cpp
+++ b/tests/test_constants_and_functions.cpp
@@ -41,6 +41,26 @@ std::string print_bytes(py::bytes bytes) {
     return ret;
 }
 
+// Test that we properly handle C++17 exception specifiers (which are part of the function signature
+// in C++17).  These should all still work before C++17, but don't affect the function signature.
+namespace test_exc_sp {
+int f1(int x) noexcept { return x+1; }
+int f2(int x) noexcept(true) { return x+2; }
+int f3(int x) noexcept(false) { return x+3; }
+int f4(int x) throw() { return x+4; } // Deprecated equivalent to noexcept(true)
+struct C {
+    int m1(int x) noexcept { return x-1; }
+    int m2(int x) const noexcept { return x-2; }
+    int m3(int x) noexcept(true) { return x-3; }
+    int m4(int x) const noexcept(true) { return x-4; }
+    int m5(int x) noexcept(false) { return x-5; }
+    int m6(int x) const noexcept(false) { return x-6; }
+    int m7(int x) throw() { return x-7; }
+    int m8(int x) const throw() { return x-8; }
+};
+}
+
+
 test_initializer constants_and_functions([](py::module &m) {
     m.attr("some_constant") = py::int_(14);
 
@@ -63,4 +83,22 @@ test_initializer constants_and_functions([](py::module &m) {
 
     m.def("return_bytes", &return_bytes);
     m.def("print_bytes", &print_bytes);
+
+    using namespace test_exc_sp;
+    py::module m2 = m.def_submodule("exc_sp");
+    py::class_<C>(m2, "C")
+        .def(py::init<>())
+        .def("m1", &C::m1)
+        .def("m2", &C::m2)
+        .def("m3", &C::m3)
+        .def("m4", &C::m4)
+        .def("m5", &C::m5)
+        .def("m6", &C::m6)
+        .def("m7", &C::m7)
+        .def("m8", &C::m8)
+        ;
+    m2.def("f1", f1);
+    m2.def("f2", f2);
+    m2.def("f3", f3);
+    m2.def("f4", f4);
 });
diff --git a/tests/test_constants_and_functions.py b/tests/test_constants_and_functions.py
index d13d3af1..2a570d2e 100644
--- a/tests/test_constants_and_functions.py
+++ b/tests/test_constants_and_functions.py
@@ -22,3 +22,22 @@ def test_bytes():
     from pybind11_tests import return_bytes, print_bytes
 
     assert print_bytes(return_bytes()) == "bytes[1 0 2 0]"
+
+
+def test_exception_specifiers():
+    from pybind11_tests.exc_sp import C, f1, f2, f3, f4
+
+    c = C()
+    assert c.m1(2) == 1
+    assert c.m2(3) == 1
+    assert c.m3(5) == 2
+    assert c.m4(7) == 3
+    assert c.m5(10) == 5
+    assert c.m6(14) == 8
+    assert c.m7(20) == 13
+    assert c.m8(29) == 21
+
+    assert f1(33) == 34
+    assert f2(53) == 55
+    assert f3(86) == 89
+    assert f4(140) == 144