The introduction of Apple Music and iCloud Music Library in iOS 8.4, like iTunes Match before it, effectively places your entire iTunes music library and more at your fingertips, rather than only the music you’ve chosen to sync to your device directly from iTunes. You can still explicitly download tracks simply by tapping on the option button beside a song, album, or playlist and choosing “Make available offline,” however anything that hasn’t been downloaded and stored on your device will be streamed from Apple’s servers. If you find this selection to be a bit overwhelming, or simply want to stick to locally stored music to save on cellular data bandwidth, you can easily filter your “My Music” section to only show music that’s actually been downloaded to your device.
From the “My Music” screen, tap on the header above your album, track, or playlist listing, and down at the bottom you’ll see a toggle to Show Music Available Offline. Turning this on will immediately filter your library to show only those tracks that are stored on your device. This also happens automatically if you put your iPhone in Airplane Mode or are otherwise away from a cellular or Wi-Fi data connection. Unfortunately, this doesn’t affect playlists – you’ll still see all of them listed, even those that don’t contain any downloaded tracks.