I see this is an older post, but after reading through all of the replies I couldn't help but add my 2cents. There is a much easier way to free up a lot of this bloated space (for those who use Apple Music), short of going through the entire process of Restoring your phone from a backup. Which takes a lot of time. You want a solution that will work quickly so you can keep taking pictures of your kid at their latest performance.
I agree, important to delete old back-ups, deleted photos, unused apps, etc.. but the quickest thing to do to free up space is to go to the phone's Settings > iTunes & App Store > tap on "Apple ID..." > sign out > then sign back in.
Granted, this is going to free up space for those who use streaming Apple Music. Probably frees up space from other cached data, but largely it will remove the cached data from streaming music (which streams but also stores on your phone). To regain access your music library, playlists, etc. you will need to go to Settings > Music > enable "iCloud Music Library" as this gets turned off when you log out of your account. Note, you'll also have to download any music you'd downloaded previously from Apple Music, as this gets wiped out when you log out. But in a pinch when trying to shoot a priceless video, it's worth it.
