diff --git a/include/xtensor/core/xmath.hpp b/include/xtensor/core/xmath.hpp
index e40536651..aa8a7b222 100644
--- a/include/xtensor/core/xmath.hpp
+++ b/include/xtensor/core/xmath.hpp
@@ -1785,6 +1785,59 @@ namespace xt
      * @defgroup  red_functions reducing functions
      */
 
+    namespace detail
+    {
+        template <class F, class E, class X, class O>
+        inline auto logical_reduce(F f, bool identity, E&& e, X&& axes, O options)
+        {
+            auto functors = make_xreducer_functor(f, xt::const_value<bool>(identity));
+            if constexpr (xtl::is_integral<std::decay_t<X>>::value)
+            {
+                return xt::reduce(std::move(functors), std::forward<E>(e), {axes}, options);
+            }
+            else
+            {
+                return xt::reduce(std::move(functors), std::forward<E>(e), std::forward<X>(axes), options);
+            }
+        }
+    }
+
+    /**
+     * @ingroup red_functions
+     * @brief Test whether any element is true along the given axes.
+     * An empty reduction yields false. With no axes argument, the scalar
+     * overload returns a bool and stops as soon as the result is known.
+     */
+    template <class E, class X, class O = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(std::negation<is_reducer_options<X>>)>
+    inline auto any(E&& e, X&& axes, O options = O())
+    {
+        return detail::logical_reduce(detail::logical_or(), false, std::forward<E>(e), std::forward<X>(axes), options);
+    }
+
+    template <class E, class I, std::size_t N, class O = DEFAULT_STRATEGY_REDUCERS>
+    inline auto any(E&& e, const I (&axes)[N], O options = O())
+    {
+        return detail::logical_reduce(detail::logical_or(), false, std::forward<E>(e), axes, options);
+    }
+
+    /**
+     * @ingroup red_functions
+     * @brief Test whether all elements are true along the given axes.
+     * An empty reduction yields true. With no axes argument, the scalar
+     * overload returns a bool and stops as soon as the result is known.
+     */
+    template <class E, class X, class O = DEFAULT_STRATEGY_REDUCERS, XTL_REQUIRES(std::negation<is_reducer_options<X>>)>
+    inline auto all(E&& e, X&& axes, O options = O())
+    {
+        return detail::logical_reduce(detail::logical_and(), true, std::forward<E>(e), std::forward<X>(axes), options);
+    }
+
+    template <class E, class I, std::size_t N, class O = DEFAULT_STRATEGY_REDUCERS>
+    inline auto all(E&& e, const I (&axes)[N], O options = O())
+    {
+        return detail::logical_reduce(detail::logical_and(), true, std::forward<E>(e), axes, options);
+    }
+
     /**
      * @ingroup red_functions
      * @brief Sum of elements over given axes.
diff --git a/include/xtensor/reducers/xreducer.hpp b/include/xtensor/reducers/xreducer.hpp
index 2c292eb9d..9eeb90477 100644
--- a/include/xtensor/reducers/xreducer.hpp
+++ b/include/xtensor/reducers/xreducer.hpp
@@ -359,6 +359,16 @@ namespace xt
             return result;
         }
 
+        // Empty slices have no first element to initialize a partial reduction.
+        if (e.size() == 0)
+        {
+            if (result.size() != 0)
+            {
+                result.fill(options_t::has_initial_value ? options.initial_value : init_fct());
+            }
+            return result;
+        }
+
         std::size_t leading_ax = axes[(e.layout() == layout_type::row_major) ? axes.size() - 1 : 0];
         auto strides_finder = e.strides().begin() + static_cast<std::ptrdiff_t>(leading_ax);
         // The computed strides contain "0" where the shape is 1 -- therefore find the next none-zero number
diff --git a/test/test_xmath.cpp b/test/test_xmath.cpp
index 982e71a1a..9d30763df 100644
--- a/test/test_xmath.cpp
+++ b/test/test_xmath.cpp
@@ -27,6 +27,59 @@ namespace xt
      * Basic operations *
      ********************/
 
+    TEST(xmath, logical_reduction_axes)
+    {
+        xarray<int> a = {{0, 0, 0}, {-1, 0, 2}};
+        static_assert(std::is_same_v<decltype(xt::any(a)), bool>);
+        static_assert(std::is_same_v<decltype(xt::all(a)), bool>);
+        auto rows = xt::any(a, -1);
+        static_assert(std::is_same_v<typename decltype(rows)::value_type, bool>);
+        EXPECT_EQ(rows.shape(), (shape_type{2}));
+        EXPECT_FALSE(rows(0));
+        EXPECT_TRUE(rows(1));
+        EXPECT_TRUE(xt::any(a, {0, 1})());
+        EXPECT_FALSE(xt::all(a, {0, 1})());
+
+        std::vector<int> axes = {0};
+        auto kept = xt::all(a + 1, axes, xt::keep_dims | xt::evaluation_strategy::immediate);
+        EXPECT_EQ(kept.shape(), (shape_type{1, 3}));
+        EXPECT_FALSE(kept(0, 0));
+        EXPECT_TRUE(kept(0, 1));
+        EXPECT_TRUE(kept(0, 2));
+
+        xarray<int> mixed = {{{0, 0}, {1, 2}}, {{0, 3}, {-1, 4}}};
+        auto columns = xt::all(mixed, {0, 2});
+        EXPECT_EQ(columns.shape(), (shape_type{2}));
+        EXPECT_FALSE(columns(0));
+        EXPECT_TRUE(columns(1));
+
+        std::vector<int> no_axes;
+        auto elementwise = xt::any(a, no_axes, xt::evaluation_strategy::immediate);
+        EXPECT_EQ(elementwise.shape(), a.shape());
+        EXPECT_FALSE(elementwise(0, 1));
+        EXPECT_TRUE(elementwise(1, 0));
+
+        const xarray<int> empty = xarray<int>::from_shape({2, 0});
+        auto none = xt::any(empty, 1);
+        auto every = xt::all(empty, 1);
+        EXPECT_FALSE(none(0));
+        EXPECT_FALSE(none(1));
+        EXPECT_TRUE(every(0));
+        EXPECT_TRUE(every(1));
+
+        auto empty_rows = xarray<int>::from_shape({0, 3});
+        auto by_column = xt::any(empty_rows, 0, xt::evaluation_strategy::immediate);
+        auto every_column = xt::all(empty_rows, 0, xt::evaluation_strategy::immediate);
+        EXPECT_EQ(by_column.shape(), (shape_type{3}));
+        EXPECT_FALSE(xt::any(by_column));
+        EXPECT_EQ(every_column.shape(), (shape_type{3}));
+        EXPECT_TRUE(xt::all(every_column));
+        EXPECT_EQ(xt::any(empty_rows, 1, xt::evaluation_strategy::immediate).size(), 0u);
+        EXPECT_EQ(xt::all(empty_rows, 1, xt::evaluation_strategy::immediate).size(), 0u);
+        auto seeded = xt::sum(empty_rows, 0, xt::initial(7) | xt::evaluation_strategy::immediate);
+        EXPECT_TRUE(xt::all(xt::equal(seeded, 7)));
+    }
+
     TEST(xmath, abs)
     {
         shape_type shape = {3, 2};