diff --git a/CMakeLists.txt b/CMakeLists.txt
index 500ce02..f1f59ff 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -57,9 +57,9 @@
 mark_as_advanced(CMAKE_CXX_STANDARD_REQUIRED)
 
 # MSVC versions < 2013 did not fully support >= C++11.
-if (MSVC AND MSVC_VERSION VERSION_LESS 1800)
-  message(FATAL_ERROR "Invalid MSVC_VERSION: ${MSVC_VERSION}. Ceres requires at "
-    "least MSVC 2013 Update 4+")
+if (MSVC AND CMAKE_CXX_COMPILER_VERSION VERSION_LESS 12.0)
+  message(FATAL_ERROR "Invalid CMAKE_CXX_COMPILER_VERSION: "
+    "${CMAKE_CXX_COMPILER_VERSION}. Ceres requires at least MSVC 2013 Update 4+")
 endif()
 
 project(Ceres C CXX)
@@ -524,35 +524,6 @@
   endif (CMAKE_BUILD_TYPE STREQUAL "Debug")
 endif (NOT CMAKE_BUILD_TYPE)
 
-# Set the default Ceres flags to an empty string.
-set (CERES_CXX_FLAGS)
-
-if (CMAKE_BUILD_TYPE STREQUAL "Release")
-  if (CMAKE_COMPILER_IS_GNUCXX)
-    # Linux
-    if (CMAKE_SYSTEM_NAME MATCHES "Linux")
-      if (NOT GCC_VERSION VERSION_LESS 4.2)
-        set (CERES_CXX_FLAGS "${CERES_CXX_FLAGS} -march=native -mtune=native")
-      endif (NOT GCC_VERSION VERSION_LESS 4.2)
-    endif (CMAKE_SYSTEM_NAME MATCHES "Linux")
-    # Mac OS X
-    if (CMAKE_SYSTEM_NAME MATCHES "Darwin")
-      set (CERES_CXX_FLAGS "${CERES_CXX_FLAGS} -msse3")
-      # Use of -fast only applicable for Apple's GCC
-      # Assume this is being used if GCC version < 4.3 on OSX
-      execute_process(COMMAND ${CMAKE_C_COMPILER}
-        ARGS ${CMAKE_CXX_COMPILER_ARG1} -dumpversion
-        OUTPUT_VARIABLE GCC_VERSION
-        OUTPUT_STRIP_TRAILING_WHITESPACE)
-      if (GCC_VERSION VERSION_LESS 4.3)
-        set (CERES_CXX_FLAGS "${CERES_CXX_FLAGS} -fast")
-      endif (GCC_VERSION VERSION_LESS 4.3)
-    endif (CMAKE_SYSTEM_NAME MATCHES "Darwin")
-  endif (CMAKE_COMPILER_IS_GNUCXX)
-endif (CMAKE_BUILD_TYPE STREQUAL "Release")
-
-set (CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} ${CERES_CXX_FLAGS}")
-
 if (MINGW)
   # MinGW produces code that segfaults when performing matrix multiplications
   # in Eigen when compiled with -O3 (see [1]), as such force the use of -O2
@@ -644,7 +615,7 @@
 # resulting in an unreasonably slow version of the blas routines. The
 # -Qunused-arguments is needed because CMake passes the inline
 # threshold to the linker and clang complains about it and dies.
-if (CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
+if (CMAKE_CXX_COMPILER_ID MATCHES "Clang") # Matches Clang & AppleClang.
   set(CMAKE_CXX_FLAGS
     "${CMAKE_CXX_FLAGS} -Qunused-arguments -mllvm -inline-threshold=600")
 
@@ -658,24 +629,6 @@
   endif(HAVE_RETURN_TYPE_C_LINKAGE)
 endif ()
 
-# Xcode 4.5.x used Clang 4.1 (Apple version), this has a bug that prevents
-# compilation of Ceres.
-if (APPLE AND CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
-  execute_process(COMMAND ${CMAKE_CXX_COMPILER}
-    ARGS ${CMAKE_CXX_COMPILER_ARG1} -dumpversion
-    OUTPUT_VARIABLE CLANG_VERSION
-    OUTPUT_STRIP_TRAILING_WHITESPACE)
-  # Use version > 4.0 & < 4.2 to catch all 4.1(.x) versions.
-  if (CLANG_VERSION VERSION_GREATER 4.0 AND
-      CLANG_VERSION VERSION_LESS 4.2)
-    message(FATAL_ERROR "You are attempting to build Ceres on OS X using Xcode "
-      "4.5.x (Clang version: ${CLANG_VERSION}). This version of Clang has a "
-      "bug that prevents compilation of Ceres, please update to "
-      "Xcode >= 4.6.3.")
-  endif (CLANG_VERSION VERSION_GREATER 4.0 AND
-    CLANG_VERSION VERSION_LESS 4.2)
-endif (APPLE AND CMAKE_CXX_COMPILER_ID STREQUAL "Clang")
-
 # Configure the Ceres config.h compile options header using the current
 # compile options and put the configured header into the Ceres build
 # directory.  Note that the ceres/internal subdir in <build>/config where
diff --git a/docs/source/installation.rst b/docs/source/installation.rst
index f9a7701..e7951bf 100644
--- a/docs/source/installation.rst
+++ b/docs/source/installation.rst
@@ -577,6 +577,34 @@
  ``CMake`` GUI.  If they are not present in the *Standard View*,
  toggle to the *Advanced View* with ``<t>``.
 
+
+Modifying default compilation flags
+-----------------------------------
+
+The ``CMAKE_CXX_FLAGS`` variable can be used to define additional
+default compilation flags for all build types.  Any flags specified
+in ``CMAKE_CXX_FLAGS`` will be used in addition to the default
+flags used by Ceres for the current build type.
+
+For example, if you wished to build Ceres with `-march=native
+<https://gcc.gnu.org/onlinedocs/gcc/x86-Options.html>`_ which is not
+enabled by default (even if ``CMAKE_BUILD_TYPE=Release``) you would invoke
+CMake with:
+
+.. code-block:: bash
+
+       cmake -DCMAKE_CXX_FLAGS="-march=native" <PATH_TO_CERES_SOURCE>
+
+.. NOTE ::
+
+    The use of ``-march=native`` will limit portability, as it will tune the
+    implementation to the specific CPU of the compiling machine (e.g. use of
+    AVX if available).  Run-time segfaults may occur if you then tried to
+    run the resulting binaries on a machine with a different processor, even
+    if it is from the same family (e.g. x86) if the specific options available
+    are different.  Note that the performance gains from the use of
+    ``-march=native`` are not guaranteed to be significant.
+
 .. _options-controlling-ceres-configuration:
 
 Options controlling Ceres configuration