In order to keep track of which images go where, I use the ‘Attach’ feature. That way I know what Library items are used on what page. It’s very basic but still a form of tagging. You can sort by it also.
Well I did figure out one way if you are on a Windows computer and you are simply uploading images files like JPG. If you ‘tag’ your images with a title before uploading to WordPress then the WordPress media library will pick up the title of the image and add it as the title of the media file in WordPress. Titles are searchable in the media library.
So in my use-case, I have a folder of images I want to upload to WordPress. These images will be used for a slideshow so I will apply a title of ‘2016.02.29MeetingPictures’ to all the images. I simply select all of the images in Windows Explorer (and with the Details Pane enabled in Explorer) I type or paste ‘2016.02.29MeetingPictures’ into the Title property for the images. Once those titles are saved I upload to media library and can find the image files simply by searching on ‘2016.02.29’ or ‘meeting’, or ‘2016.02.29MeetingPictures’.
It would be great if the media library were able to read the tags for the images but it does not appear to do it.
So maybe not the most beautiful solution but works for what I need.