Android/iOS: FREEdi YouTube Player enables videos in the background, so you can close the video you're watching and keep listening to the audio.
One of the biggest annoyances of the native YouTube app is that you have to keep the app open to keep the video playing. FREEdi is one of the few alternatives that eradicates this setback. In addition, you can make your own playlists from the app and set a sleep timer to automatically stop playing a playlist when you're ready. There's also a repeat mode.
The app is free in the Google Play Store.