Upon arriving at work in care work Spotify to listen to albums, playlists, and radio stations etc, at the end of the day when I'm coming home I take my smartphone to hear more songs on the way, but Spotify still not the music that I was listening Desktop, not remains to radio, it just stopped this last song I heard on my smartphone but not the last song, playlist or radio that my user was listening.
I own several dispositos connected to Spotify but I'm a single user, I want a continuation of exepriência.
This is a feature that really bothers me on Spotify and one that I liked at Rdio.
As @johannesdr mentioned, you can already do that with Spotify Connect (premium feature). Please follow the links in his comment for more information about it.
Also any news when it roles out to the desktop officially will be announced here: