Media Library modal customization

By default, in the Media Upload Modal Box you can only filter by Date (Month uploaded) and/or Search. To fully take advantage of the search function you should have proper filenames, alt text and description of every image when you upload them.

For pagination you can go to your Media Gallery and turn on List Mode:

Or directly by visiting: https://yoursite.com/wp-admin/upload.php?mode=list

If you want to customize the modal box and extend its functionality to filter by taxonomies like this:

please have a look at this answer. You can find the full code for Media Taxonomies at GitHub here.