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<!-- For your functions.php file or a functionality plugin: -->

function cc_mime_types($mimes) {
  $mimes['svg'] = 'image/svg+xml';
  return $mimes;
}
add_filter('upload_mimes', 'cc_mime_types');

<!-- Without this, SVG files will be rejected when attempting to upload them through the media uploader. -->

<!-- Before WordPress 4.0, you also make them display properly in the Media grid. But that's broken now. If anyone knows how to fix, let me know! -->

function fix_svg_thumb_display() {
  echo '
    td.media-icon img[src$=".svg"], img[src$=".svg"].attachment-post-thumbnail { 
      width: 100% !important; 
      height: auto !important; 
    }
  ';
}
add_action('admin_head', 'fix_svg_thumb_display');