This free plugin by ZigPress for ClassicPress and WordPress adds categories and tags to items in the Media Library.
You can add and remove categories and tags by editing a media item in list view, and you can also bulk add and remove categories and tags using the Bulk Actions dropdown on the Media Library page.
ZP Media Taxonomies also adds a new column to the Media Library list view, showing the file size and image dimensions.
You can choose below whether to use dedicated taxonomies (recommended) or the built-in taxonomies used for posts. If you use the built-in taxonomies then your categories and tags will be shared across posts and media items, however there will be no tag filter dropdown and the category filter dropdown will not show counts.
The download link on the right is a direct link to the zip of the current release. To install the plugin, download this zip then go to the admin plugins page, click the ‘Add New’ button, then click the ‘Upload Plugin’ button and upload the zip file.
Though this plugin is not in the WordPress plugin repository, future updates will be shown on the admin plugins page when available. The plugin must be active in order to check for updates.