diff --git a/include/alpaka/mem/MdSpan.hpp b/include/alpaka/mem/MdSpan.hpp
index 4cae1629..8ea17658 100644
--- a/include/alpaka/mem/MdSpan.hpp
+++ b/include/alpaka/mem/MdSpan.hpp
@@ -112,11 +112,21 @@ namespace alpaka
         }
 
         constexpr auto begin() const
+        {
+            return MdForwardIter{this->getConstMdSpan()};
+        }
+
+        constexpr auto begin()
         {
             return MdForwardIter{*this};
         }
 
         constexpr auto end() const
+        {
+            return MdForwardIterEnd{this->getConstMdSpan()};
+        }
+
+        constexpr auto end()
         {
             return MdForwardIterEnd{*this};
         }
diff --git a/include/alpaka/mem/MdSpanArray.hpp b/include/alpaka/mem/MdSpanArray.hpp
index 75a418ff..f788cbca 100644
--- a/include/alpaka/mem/MdSpanArray.hpp
+++ b/include/alpaka/mem/MdSpanArray.hpp
@@ -108,11 +108,21 @@ namespace alpaka
         }
 
         constexpr auto begin() const
+        {
+            return MdForwardIter{this->getConstMdSpan()};
+        }
+
+        constexpr auto begin()
         {
             return MdForwardIter{*this};
         }
 
         constexpr auto end() const
+        {
+            return MdForwardIterEnd{this->getConstMdSpan()};
+        }
+
+        constexpr auto end()
         {
             return MdForwardIterEnd{*this};
         }
diff --git a/test/unit/mem/mdIterator.cpp b/test/unit/mem/mdIterator.cpp
index cdbc4da9..043fc725 100644
--- a/test/unit/mem/mdIterator.cpp
+++ b/test/unit/mem/mdIterator.cpp
@@ -6,29 +6,124 @@
 
 #include <catch2/catch_test_macros.hpp>
 
+#include <array>
+#include <type_traits>
+#include <utility>
+#include <vector>
 
 using namespace alpaka;
 using namespace alpaka::onHost;
 
-TEST_CASE("mdIterator", "")
+TEST_CASE("mdIterator host coverage", "[mem][mdIterator][iterator]")
 {
-    constexpr auto numElements = CVec<size_t, 17, 31>{};
-    alpaka::concepts::IBuffer auto span = onHost::allocHost<uint32_t>(numElements);
+    auto collectValues = []<typename T_Range>(T_Range&& range)
+    {
+        using Value = std::remove_cvref_t<decltype(*range.begin())>;
+        std::vector<Value> values;
+        for(auto&& value : range)
+            values.push_back(value);
+        return values;
+    };
+
+    SECTION("zero-extent MdSpan and View are empty")
+    {
+        // Zero extents should terminate immediately instead of yielding a bogus first element.
+        std::array<uint32_t, 1> storage{42u};
+        auto const emptyMdSpan = alpaka::makeMdSpan(storage.data(), alpaka::Vec{0u, 3u});
+        auto const emptyView = alpaka::makeView(api::host, storage.data(), alpaka::Vec{0u, 3u});
+
+        REQUIRE(emptyMdSpan.begin() == emptyMdSpan.end());
+        REQUIRE(emptyView.begin() == emptyView.end());
+        REQUIRE(collectValues(emptyMdSpan).empty());
+        REQUIRE(collectValues(emptyView).empty());
+    }
+
+    SECTION("1D MdSpan iteration stays linear")
+    {
+        // A linear buffer should be visited in storage order on the host path.
+        std::array<uint32_t, 5> storage{3u, 6u, 9u, 12u, 15u};
+        auto span = alpaka::makeMdSpan(storage.data(), alpaka::Vec{storage.size()});
 
-    size_t counter = 0u;
-    for(uint32_t& v : span)
-        v = counter++;
+        REQUIRE(collectValues(span) == std::vector<uint32_t>{3u, 6u, 9u, 12u, 15u});
+    }
 
-    // validate by using the forward iterator
-    size_t refence = 0u;
-    for(uint32_t v : span)
+    SECTION("3D View iteration follows linearize order")
     {
-        CHECK(v == refence);
-        ++refence;
+        // The iterator must keep the last dimension fastest so traversal matches linearized indexing.
+        auto const extents = alpaka::Vec{2u, 3u, 4u};
+        auto buffer = onHost::allocHost<uint32_t>(extents);
+        auto view = buffer.getView();
+
+        meta::ndLoopIncIdx(
+            extents,
+            [&](alpaka::concepts::Vector<uint32_t, 3> auto idx)
+            { view[idx] = static_cast<uint32_t>(linearize(extents, idx)); });
+
+        auto const visited = collectValues(view);
+        REQUIRE(visited.size() == extents.product());
+        REQUIRE(visited.front() == 0u);
+        REQUIRE(visited.back() == extents.product() - 1u);
+
+        for(uint32_t linearIdx = 0; linearIdx < visited.size(); ++linearIdx)
+            CHECK(visited[linearIdx] == linearIdx);
     }
 
-    // validate without using the forward iterator
-    meta::ndLoopIncIdx(
-        numElements,
-        [&](alpaka::concepts::Vector<size_t, 2> auto idx) { CHECK(span[idx] == linearize(numElements, idx)); });
+    SECTION("mutable View iteration writes back into the underlying buffer")
+    {
+        // Writing through a non-const iterator must update the storage the view refers to.
+        auto const extents = alpaka::Vec{2u, 3u};
+        auto buffer = onHost::allocHost<int>(extents);
+        auto view = buffer.getView();
+
+        int nextValue = 10;
+        for(int& value : view)
+        {
+            value = nextValue;
+            nextValue += 5;
+        }
+
+        REQUIRE(view[alpaka::Vec{0u, 0u}] == 10);
+        REQUIRE(view[alpaka::Vec{0u, 2u}] == 20);
+        REQUIRE(view[alpaka::Vec{1u, 0u}] == 25);
+        REQUIRE(view[alpaka::Vec{1u, 2u}] == 35);
+        CHECK(buffer[alpaka::Vec{1u, 1u}] == 30);
+    }
+
+    SECTION("const View iteration is read-only and preserves order")
+    {
+        // Const iteration should expose const references while traversing the same order as mutable iteration.
+        std::array<int, 6> storage{2, 4, 6, 8, 10, 12};
+        auto view = alpaka::makeView(api::host, storage.data(), alpaka::Vec{2u, 3u});
+        auto const constView = view.getConstView();
+
+        static_assert(!std::is_const_v<std::remove_reference_t<decltype(*view.begin())>>);
+        static_assert(std::is_const_v<std::remove_reference_t<decltype(*constView.begin())>>);
+        static_assert(std::is_const_v<std::remove_reference_t<decltype(*std::as_const(view).begin())>>);
+
+        REQUIRE(collectValues(view) == std::vector<int>{2, 4, 6, 8, 10, 12});
+        REQUIRE(collectValues(constView) == collectValues(view));
+    }
+
+    SECTION("pre-increment and post-increment advance one element at a time")
+    {
+        // Forward-iterator increments need to preserve the old value for post-increment and return self for pre-increment.
+        std::array<int, 4> storage{7, 11, 13, 17};
+        auto span = alpaka::makeMdSpan(storage.data(), alpaka::Vec{storage.size()});
+
+        auto iter = span.begin();
+        REQUIRE(*iter == 7);
+
+        auto& preIncrement = ++iter;
+        REQUIRE(&preIncrement == &iter);
+        REQUIRE(*iter == 11);
+
+        auto postIncrement = iter++;
+        REQUIRE(*postIncrement == 11);
+        REQUIRE(*iter == 13);
+
+        ++iter;
+        REQUIRE(*iter == 17);
+        ++iter;
+        REQUIRE(iter == span.end());
+    }
 }