diff --git a/include/boost/mp11/algorithm.hpp b/include/boost/mp11/algorithm.hpp
index e717368..a25f48f 100644
--- a/include/boost/mp11/algorithm.hpp
+++ b/include/boost/mp11/algorithm.hpp
@@ -1,7 +1,7 @@
 #ifndef BOOST_MP11_ALGORITHM_HPP_INCLUDED
 #define BOOST_MP11_ALGORITHM_HPP_INCLUDED
 
-//  Copyright 2015, 2016 Peter Dimov.
+//  Copyright 2015-2017 Peter Dimov.
 //
 //  Distributed under the Boost Software License, Version 1.0.
 //
@@ -69,6 +69,31 @@ template<template<class...> class F, template<class...> class L1, class... T1, t
 
 template<template<class...> class F, class... L> using mp_transform = typename detail::mp_transform_impl<F, L...>::type;
 
+// mp_transform_if<P, F, L>
+namespace detail
+{
+
+template<template<class...> class P, template<class...> class F, class L> struct mp_transform_if_impl;
+
+template<template<class...> class P, template<class...> class F, template<class...> class L, class... T> struct mp_transform_if_impl<P, F, L<T...>>
+{
+#if defined( BOOST_MSVC ) && BOOST_WORKAROUND( BOOST_MSVC, <= 1910 )
+
+    template<class U> struct _f { using type = mp_eval_if<mp_not<P<U>>, U, F, U>; };
+    using type = L<typename _f<T>::type...>;
+
+#else
+
+    template<class U> using _f = mp_eval_if<mp_not<P<U>>, U, F, U>;
+    using type = L<_f<T>...>;
+
+#endif
+};
+
+} // namespace detail
+
+template<template<class...> class P, template<class...> class F, class L> using mp_transform_if = typename detail::mp_transform_if_impl<P, F, L>::type;
+
 // mp_fill<L, V>
 namespace detail
 {
diff --git a/include/boost/mp11/map.hpp b/include/boost/mp11/map.hpp
index 30c4a64..9350b70 100644
--- a/include/boost/mp11/map.hpp
+++ b/include/boost/mp11/map.hpp
@@ -1,7 +1,7 @@
 #ifndef BOOST_MP11_MAP_HPP_INCLUDED
 #define BOOST_MP11_MAP_HPP_INCLUDED
 
-//  Copyright 2015, 2016 Peter Dimov.
+//  Copyright 2015-2017 Peter Dimov.
 //
 //  Distributed under the Boost Software License, Version 1.0.
 //
@@ -46,6 +46,26 @@ template<template<class...> class M, class... U, class T> struct mp_map_replace_
 template<class M, class T> using mp_map_replace = typename detail::mp_map_replace_impl<M, T>::type;
 
 // mp_map_update<M, T, F>
+namespace detail
+{
+
+template<class M, class T, template<class...> class F> struct mp_map_update_impl
+{
+    template<class U> using _f = std::is_same<mp_first<T>, mp_first<U>>;
+
+    // _f2<L<X, Y...>> -> F<Y...>
+    // _f2<pair<X, Y>> -> F<Y>
+    template<class L> using _f2 = mp_rename<mp_rest<mp_rename<L, mp_list>>, F>;
+
+    // _f3<L<X, Y...>> -> L<X, F<Y...>>
+    template<class L> using _f3 = mp_assign<L, mp_list<mp_first<L>, _f2<L>>>;
+
+    using type = mp_if< mp_map_contains<M, mp_first<T>>, mp_transform_if<_f, _f3, M>, mp_push_back<M, T> >;
+};
+
+} // namespace detail
+
+template<class M, class T, template<class...> class F> using mp_map_update = typename detail::mp_map_update_impl<M, T, F>::type;
 
 // mp_map_erase<M, K>
 namespace detail
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 48b993b..b00e64c 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -30,6 +30,7 @@ run mp_append.cpp : : : $(REQ) ;
 run mp_assign.cpp : : : $(REQ) ;
 run mp_clear.cpp : : : $(REQ) ;
 run mp_transform.cpp : : : $(REQ) ;
+run mp_transform_if.cpp : : : $(REQ) ;
 run mp_fill.cpp : : : $(REQ) ;
 run mp_count.cpp : : : $(REQ) ;
 run mp_count_if.cpp : : : $(REQ) ;
@@ -95,3 +96,4 @@ run mp_map_contains.cpp : : : $(REQ) ;
 run mp_map_insert.cpp : : : $(REQ) ;
 run mp_map_replace.cpp : : : $(REQ) ;
 run mp_map_erase.cpp : : : $(REQ) ;
+run mp_map_update.cpp : : : $(REQ) ;
diff --git a/test/mp_map_erase.cpp b/test/mp_map_erase.cpp
index c03ffc8..466f4c9 100644
--- a/test/mp_map_erase.cpp
+++ b/test/mp_map_erase.cpp
@@ -18,7 +18,6 @@ int main()
 {
     using boost::mp_map_erase;
     using boost::mp_list;
-    using boost::mp_push_back;
 
     BOOST_TEST_TRAIT_TRUE((std::is_same<mp_map_erase<mp_list<>, void>, mp_list<>>));
     BOOST_TEST_TRAIT_TRUE((std::is_same<mp_map_erase<std::tuple<>, int>, std::tuple<>>));
diff --git a/test/mp_map_update.cpp b/test/mp_map_update.cpp
new file mode 100644
index 0000000..d957806
--- /dev/null
+++ b/test/mp_map_update.cpp
@@ -0,0 +1,48 @@
+
+// Copyright 2016, 2017 Peter Dimov.
+//
+// Distributed under the Boost Software License, Version 1.0.
+//
+// See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+
+
+#include <boost/mp11/map.hpp>
+#include <boost/mp11/list.hpp>
+#include <boost/mp11/integral.hpp>
+#include <boost/core/lightweight_test_trait.hpp>
+#include <type_traits>
+#include <tuple>
+#include <utility>
+
+using boost::mp_int;
+
+template<class T> using inc = mp_int<T::value + 1>;
+
+int main()
+{
+    using boost::mp_map_update;
+    using boost::mp_list;
+
+    using M1 = mp_list<>;
+
+    using M2 = mp_map_update< M1, std::pair<char, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M2, mp_list<std::pair<char, mp_int<0>>>>));
+
+    using M3 = mp_map_update< M2, std::pair<char, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M3, mp_list<std::pair<char, mp_int<1>>>>));
+
+    using M4 = mp_map_update< M3, std::pair<int, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M4, mp_list<std::pair<char, mp_int<1>>, std::pair<int, mp_int<0>>>>));
+
+    using M5 = mp_map_update< M4, std::pair<long, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M5, mp_list<std::pair<char, mp_int<1>>, std::pair<int, mp_int<0>>, std::pair<long, mp_int<0>>>>));
+
+    using M6 = mp_map_update< M5, std::pair<long, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M6, mp_list<std::pair<char, mp_int<1>>, std::pair<int, mp_int<0>>, std::pair<long, mp_int<1>>>>));
+
+    using M7 = mp_map_update< M6, std::pair<char, mp_int<0>>, inc >;
+    BOOST_TEST_TRAIT_TRUE((std::is_same<M7, mp_list<std::pair<char, mp_int<2>>, std::pair<int, mp_int<0>>, std::pair<long, mp_int<1>>>>));
+
+    return boost::report_errors();
+}
diff --git a/test/mp_transform_if.cpp b/test/mp_transform_if.cpp
new file mode 100644
index 0000000..99b6bb7
--- /dev/null
+++ b/test/mp_transform_if.cpp
@@ -0,0 +1,46 @@
+
+//  Copyright 2015, 2017 Peter Dimov.
+//
+// Distributed under the Boost Software License, Version 1.0.
+//
+// See accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt
+
+
+#include <boost/mp11/algorithm.hpp>
+#include <boost/mp11/list.hpp>
+#include <boost/mp11/integral.hpp>
+#include <boost/core/lightweight_test_trait.hpp>
+#include <type_traits>
+#include <tuple>
+#include <utility>
+
+struct X1 {};
+struct X2 {};
+struct X3 {};
+struct X4 {};
+
+template<class T> using add_pointer = T*;
+template<class T> using is_not_ref = boost::mp_not<std::is_reference<T>>;
+
+int main()
+{
+    using boost::mp_list;
+    using boost::mp_transform_if;
+
+    using L1 = mp_list<X1, X2&, X3 const, X4 const&>;
+
+    BOOST_TEST_TRAIT_TRUE((std::is_same<mp_transform_if<is_not_ref, add_pointer, L1>, mp_list<X1*, X2&, X3 const*, X4 const&>>));
+
+    using L2 = std::tuple<X1, X2&, X3 const, X4 const&>;
+
+    BOOST_TEST_TRAIT_TRUE((std::is_same<mp_transform_if<is_not_ref, add_pointer, L2>, std::tuple<X1*, X2&, X3 const*, X4 const&>>));
+
+    using L3 = std::pair<X1 const, X2&>;
+
+    BOOST_TEST_TRAIT_TRUE((std::is_same<mp_transform_if<is_not_ref, add_pointer, L3>, std::pair<X1 const*, X2&>>));
+
+    //
+
+    return boost::report_errors();
+}