Running with Apple Watch.
So I am looking into buying an Apple Watch. If I were to go for a run, could I connect my watch to my headphones and listen to Spotify from my watch while leaving my phone at home?
Spotify does Not support playing music on the Apple Watch.
You can use Pandora (streaming or offline playlists), Apple Music (streaming or offline playlists), or transfer your own music from your iPhone to the Apple Watch.
But Spotify has choosen to Not support the Apple Watch. If you want Spotify, you need to contact Spotify and let them know your desires.
