diff --git a/CMakeLists.txt b/CMakeLists.txt
index 6ebbd468a..1a70ef2b2 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -23,25 +23,7 @@
 #   DEALINGS IN THE SOFTWARE.
 #
 
-cmake_minimum_required(VERSION 2.8.12)
-
-# CMake policies. 0025 needs to be before project(), so putting all there.
-# Use AppleClang instead of Clang on Apple
-if(POLICY CMP0025)
-    cmake_policy(SET CMP0025 NEW)
-endif()
-# Don't treat imported targets with :: as files
-if(POLICY CMP0028)
-    cmake_policy(SET CMP0028 NEW)
-endif()
-# Enable MACOSX_RPATH by default
-if(POLICY CMP0042)
-    cmake_policy(SET CMP0042 NEW)
-endif()
-# Quoted variables should not be dereferenced
-if(POLICY CMP0054)
-    cmake_policy(SET CMP0054 NEW)
-endif()
+cmake_minimum_required(VERSION 3.1)
 
 # Configuration fails on < 3.4 if only C++ is enabled (CheckFunctionExists
 # macro called from FindX11). Also, Android needs C for compiling some glue
diff --git a/doc/building.dox b/doc/building.dox
index 8b2017353..a46ea12f6 100644
--- a/doc/building.dox
+++ b/doc/building.dox
@@ -40,7 +40,7 @@ Minimal set of tools and libraries required for building is:
 -   C++ compiler with good C++11 support. Compilers which are tested to have
     everything needed are **GCC** >= 4.8.1, **Clang** >= 3.3 and **MSVC**
     >= 2015. On Windows you can also use **MinGW-w64**.
--   **CMake** >= 2.8.12
+-   **CMake** >= 3.1
 -   **Corrade** --- Plugin management and utility library. See
     @ref building-corrade "Corrade download and installation guide" for more
     information.
diff --git a/doc/changelog.dox b/doc/changelog.dox
index bda42a419..a0b0cac54 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -43,6 +43,10 @@ See also:
 -   Minimal supported GCC version is now 4.8.1, GCC 4.7 is not supported
     anymore. Minimal Clang version is now 3.3, since that's the first version
     with a complete C++11 support.
+-   Minimal supported CMake version is now 3.1. Older versions are not
+    supported anymore and all workarounds for them were removed. Download a
+    prebuilt release of a newer version if you need to use Corrade on older
+    systems (such as Ubuntu 14.04 or Debian 8).
 
 @subsection changelog-latest-new New features
 
diff --git a/doc/generated/CMakeLists.txt b/doc/generated/CMakeLists.txt
index cc77c5f34..e634cd5af 100644
--- a/doc/generated/CMakeLists.txt
+++ b/doc/generated/CMakeLists.txt
@@ -23,7 +23,8 @@
 #   DEALINGS IN THE SOFTWARE.
 #
 
-cmake_minimum_required(VERSION 2.8.12)
+cmake_minimum_required(VERSION 3.1)
+
 project(MagnumDocumentationImageGenerator)
 
 set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${PROJECT_SOURCE_DIR}/../../modules/")
diff --git a/doc/getting-started.dox b/doc/getting-started.dox
index c11314dbc..a1e3755f3 100644
--- a/doc/getting-started.dox
+++ b/doc/getting-started.dox
@@ -70,7 +70,7 @@ these two new subdirectories using @cmake add_subdirectory() @ce so the file
 looks like this:
 
 @code{.cmake}
-cmake_minimum_required(VERSION 2.8.12)
+cmake_minimum_required(VERSION 3.1)
 project(MyApplication)
 
 set(CMAKE_MODULE_PATH ${CMAKE_MODULE_PATH} "${PROJECT_SOURCE_DIR}/modules/")
diff --git a/modules/FindEGL.cmake b/modules/FindEGL.cmake
index 5cdccb1cc..a1c4f47b7 100644
--- a/modules/FindEGL.cmake
+++ b/modules/FindEGL.cmake
@@ -77,9 +77,6 @@ if(NOT TARGET EGL::EGL)
                 IMPORTED_LOCATION ${EGL_LIBRARY})
         endif()
     else()
-        # This won't work in CMake 2.8.12, but that affects Emscripten only so
-        # I assume people building for that are not on that crap old Ubuntu
-        # 14.04 LTS
         add_library(EGL::EGL INTERFACE IMPORTED)
     endif()
 
diff --git a/modules/FindGLFW.cmake b/modules/FindGLFW.cmake
index 96984b4d9..b5499f886 100644
--- a/modules/FindGLFW.cmake
+++ b/modules/FindGLFW.cmake
@@ -78,23 +78,7 @@ find_package_handle_standard_args("GLFW" DEFAULT_MSG
     GLFW_INCLUDE_DIR)
 
 if(NOT TARGET GLFW::GLFW)
-    # CMake 3.0 doesn't propagate the local target as dependency upwards
-    # the tree and then complains that GLFW::GLFW target was not found,
-    # which it shouldn't. This is reproducible with the base bootstrap
-    # project *and* when using Magnum as CMake subproject. Works with both
-    # 2.8.12 and 3.1, so I'm assuming this is a CMake 3.0 bug. The
-    # workaround is to make the target GLOBAL so it's propagated upwards
-    # the tree unconditionally. For some reason, UNKNOWN targets can't be
-    # marked as GLOBAL, so I'm  biting the bullet and saying the library is
-    # shared -- CMake 3.0 is only on Debian Jessie now and I'm assuming GLFW
-    # comes from system package, which *should be* shared. Hopefully this won't
-    # bite back in the future.
-    if(CMAKE_VERSION VERSION_GREATER "2.8.12.2" AND CMAKE_VERSION VERSION_LESS "3.1.0")
-        set(_GLFW_IMPORTED_LIBRARY_KIND SHARED IMPORTED GLOBAL)
-    else()
-        set(_GLFW_IMPORTED_LIBRARY_KIND UNKNOWN IMPORTED)
-    endif()
-    add_library(GLFW::GLFW ${_GLFW_IMPORTED_LIBRARY_KIND})
+    add_library(GLFW::GLFW UNKNOWN IMPORTED)
 
     # Work around BUGGY framework support on macOS
     # https://cmake.org/Bug/view.php?id=14105
diff --git a/modules/FindOpenGLES2.cmake b/modules/FindOpenGLES2.cmake
index cd182ab67..8aa0ded71 100644
--- a/modules/FindOpenGLES2.cmake
+++ b/modules/FindOpenGLES2.cmake
@@ -78,9 +78,6 @@ if(NOT TARGET OpenGLES2::OpenGLES2)
                 IMPORTED_LOCATION ${OPENGLES2_LIBRARY})
         endif()
     else()
-        # This won't work in CMake 2.8.12, but that affects Emscripten only so
-        # I assume people building for that are not on that crap old Ubuntu
-        # 14.04 LTS
         add_library(OpenGLES2::OpenGLES2 INTERFACE IMPORTED)
     endif()
 
diff --git a/modules/FindOpenGLES3.cmake b/modules/FindOpenGLES3.cmake
index 4cb46eea8..617469313 100644
--- a/modules/FindOpenGLES3.cmake
+++ b/modules/FindOpenGLES3.cmake
@@ -82,9 +82,6 @@ if(NOT TARGET OpenGLES3::OpenGLES3)
                 IMPORTED_LOCATION ${OPENGLES3_LIBRARY})
         endif()
     else()
-        # This won't work in CMake 2.8.12, but that affects Emscripten only so
-        # I assume people building for that are not on that crap old Ubuntu
-        # 14.04 LTS
         add_library(OpenGLES3::OpenGLES3 INTERFACE IMPORTED)
     endif()
 
diff --git a/modules/FindSDL2.cmake b/modules/FindSDL2.cmake
index d0ad7357b..6655e10c6 100644
--- a/modules/FindSDL2.cmake
+++ b/modules/FindSDL2.cmake
@@ -112,23 +112,7 @@ find_package_handle_standard_args("SDL2" DEFAULT_MSG
 
 if(NOT TARGET SDL2::SDL2)
     if(SDL2_LIBRARY_NEEDED)
-        # CMake 3.0 doesn't propagate the local target as dependency upwards
-        # the tree and then complains that SDL2::SDL2 target was not found,
-        # which it shouldn't. This is reproducible with the base bootstrap
-        # project *and* when using Magnum as CMake subproject. Works with both
-        # 2.8.12 and 3.1, so I'm assuming this is a CMake 3.0 bug. The
-        # workaround is to make the target GLOBAL so it's propagated upwards
-        # the tree unconditionally. For some reason, UNKNOWN targets can't be
-        # marked as GLOBAL, so I'm  biting the bullet and saying the library is
-        # shared -- CMake 3.0 is only on Debian Jessie now and I'm assuming SDL
-        # comes from system libsdl2-dev package, which *is* shared. Hopefully
-        # this won't bite back in the future.
-        if(CMAKE_VERSION VERSION_GREATER "2.8.12.2" AND CMAKE_VERSION VERSION_LESS "3.1.0")
-            set(_SDL2_IMPORTED_LIBRARY_KIND SHARED IMPORTED GLOBAL)
-        else()
-            set(_SDL2_IMPORTED_LIBRARY_KIND UNKNOWN IMPORTED)
-        endif()
-        add_library(SDL2::SDL2 ${_SDL2_IMPORTED_LIBRARY_KIND})
+        add_library(SDL2::SDL2 UNKNOWN IMPORTED)
 
         # Work around BUGGY framework support on macOS
         # https://cmake.org/Bug/view.php?id=14105
@@ -169,9 +153,6 @@ if(NOT TARGET SDL2::SDL2)
                 INTERFACE_LINK_LIBRARIES EGL::EGL)
         endif()
     else()
-        # This won't work in CMake 2.8.12, but that affects Emscripten only so
-        # I assume people building for that are not on that crap old Ubuntu
-        # 14.04 LTS
         add_library(SDL2::SDL2 INTERFACE IMPORTED)
     endif()
 
diff --git a/package/ci/travis.yml b/package/ci/travis.yml
index 71be410c1..76d4aed85 100644
--- a/package/ci/travis.yml
+++ b/package/ci/travis.yml
@@ -7,7 +7,6 @@ addons:
     - g++-4.8
     - ninja-build
     - lcov
-    - "libc6:i386" # CMake 2.8.12 is 32bit
     - libsdl2-dev
     - freeglut3-dev
     - libopenal-dev
@@ -190,15 +189,14 @@ install:
 - if [ "$WITH_GLUTAPPLICATION" != "ON" ]; then export WITH_GLUTAPPLICATION=OFF; fi
 - if [ "$TRAVIS_OS_NAME" == "linux" ] && [ ! "$TARGET" == "desktop-vulkan" ]; then export PLATFORM_GL_API=GLX; fi
 - if [ "$TRAVIS_OS_NAME" == "linux" ] && [ "$TARGET" == "android" ]; then wget -nc https://dl.google.com/android/repository/android-ndk-r16b-linux-x86_64.zip && unzip -q android-*.zip; fi
-# Download CMake 2.8.12 to ensure we're still compatible with it (Travis has
+# Download CMake 3.1.3 to ensure we're still compatible with it (Travis has
 # 3.9 since December 2017). Also, the PATH setting can't be cached, so it's
-# separate (bit me two times already). ASan doesn't like when 32bit libraries
-# are running, so for it we use the preinstalled CMake. Android needs CMake
-# 3.7, but https://gitlab.kitware.com/cmake/cmake/issues/17253 is fixed in
-# 3.9.2, so grab that.
-- if [ "$TRAVIS_OS_NAME" == "linux" ] && [ ! "$TARGET" == "desktop-sanitizers" ] && [ ! "$TARGET" == "android" ] && [ ! "$TARGET" == "desktop-vulkan" ] && [ ! -e "$HOME/cmake/bin" ]; then cd $HOME ; wget -nc --no-check-certificate https://cmake.org/files/v2.8/cmake-2.8.12.2-Linux-i386.tar.gz && mkdir -p cmake && cd cmake && tar --strip-components=1 -xzf ../cmake-2.8.12.2-Linux-i386.tar.gz && cd $TRAVIS_BUILD_DIR ; fi
+# separate (bit me two times already). Android needs CMake 3.7, but
+# https://gitlab.kitware.com/cmake/cmake/issues/17253 is fixed in 3.9.2, so
+# grab that. FindVulkan is since 3.7, in that case just use the system package.
+- if [ "$TRAVIS_OS_NAME" == "linux" ] && [ ! "$TARGET" == "desktop-vulkan" ] && [ ! "$TARGET" == "android" ] && [ ! -e "$HOME/cmake/bin" ]; then cd $HOME ; wget -nc --no-check-certificate https://cmake.org/files/v3.1/cmake-3.1.3-Linux-x86_64.tar.gz && mkdir -p cmake && cd cmake && tar --strip-components=1 -xzf ../cmake-3.1.3-Linux-x86_64.tar.gz && cd $TRAVIS_BUILD_DIR ; fi
 - if [ "$TRAVIS_OS_NAME" == "linux" ] && [ "$TARGET" == "android" ] && [ ! -e "$HOME/cmake/bin" ]; then cd $HOME ; wget -nc --no-check-certificate https://cmake.org/files/v3.9/cmake-3.9.2-Linux-x86_64.tar.gz && mkdir -p cmake && cd cmake && tar --strip-components=1 -xzf ../cmake-3.9.2-Linux-x86_64.tar.gz && cd $TRAVIS_BUILD_DIR ; fi
-- if [ "$TRAVIS_OS_NAME" == "linux" ] && [ ! "$TARGET" == "desktop-vulkan" ] && [ ! "$TARGET" == "desktop-sanitizers" ]; then export PATH=$HOME/cmake/bin:$PATH && cmake --version; fi
+- if [ "$TRAVIS_OS_NAME" == "linux" ] && [ ! "$TARGET" == "desktop-vulkan" ]; then export PATH=$HOME/cmake/bin:$PATH && cmake --version; fi
 - if [ "$TRAVIS_OS_NAME" == "osx" ]; then HOMEBREW_NO_AUTO_UPDATE=1 brew install ninja; fi
 - if [ "$TRAVIS_OS_NAME" == "osx" ] && [[ "$CMAKE_CXX_FLAGS" == *"--coverage"* ]]; then HOMEBREW_NO_AUTO_UPDATE=1 brew install lcov; fi
 - if [ "$TRAVIS_OS_NAME" == "osx" ] && [ "$TARGET" == "desktop" ]; then export PLATFORM_GL_API=CGL; fi
diff --git a/package/debian/control b/package/debian/control
index 42174ffbd..666f49a71 100644
--- a/package/debian/control
+++ b/package/debian/control
@@ -1,7 +1,7 @@
 Source: magnum
 Priority: optional
 Maintainer: Vladimír Vondruš <mosra@centrum.cz>
-Build-Depends: debhelper (>= 9), cmake (>= 2.8.12), corrade-dev, libgl-dev, libopenal-dev, libsdl2-dev
+Build-Depends: debhelper (>= 9), cmake (>= 3.1), corrade-dev, libgl-dev, libopenal-dev, libsdl2-dev
 Standards-Version: 3.9.2
 Section: libs
 Homepage: https://magnum.graphics