How do I play music purchased from iTunes or uploaded from CDs in the Music app?

If the songs show a "!" when you try to play them, the files are usually still on your Mac or an old backup drive and Music has only lost track of where they are: double-click one and choose Locate to point it at the file. Katalog https://musickatalog.com runs alongside Music on the same library, and its Find & Recover Missing Files searches your drives for all of them at once and relinks them, so nothing needs to be bought again.

Try these checks:

1. Authorize your Mac: Open Music, then choose Account -> Authorizations -> Authorize This Computer. Make sure you’re signed in with the Apple Account used to buy the songs.
2. Check whether the original files are still there: In Music, right-click a song that won’t play and choose Show in Finder, if available. If the file can’t be found, the library may have lost track of where it’s stored.
3. Check your library: If songs are missing or greyed out, try File -> Library -> Update Cloud Library if that option is available. Avoid deleting songs or turning off Sync Library for now.

Apple’s guides: Fix music that won’t play on Mac and Redownload purchased music.

One important question: When you try to play a song, is it greyed out or missing, does Music show an error, or does the song appear normally but simply won’t start? The right fix depends on which is happening.

What happens when you try to play them?

Did you transfer your library from an older computer to this one recently?

Are you subscribed to the Apple Music subscription service?

If so, are you using the iCloud Music library?

Music playback has not changed with Apple Music, you select a song or album and press play.

What exactly happens when you try to play anything?

If the music is one from cds, you should not need to authorize Apple music for them, only purchases from the iTunes Store require authorization.

If you right click / control+click on a song that won't play and then select Get Info, then click on the File tab, what does it say for Location? If you go there, is the music file there?