A lot of people on this thread are asking for the songs in the discovery playlist to be posted...
Just to clarify this would be pointless as everyone's Discover Weekly is unique to them.
For the future all you need to do every Monday is copy all the songs in Discover Weekly (they automatically change on mondays) to one of your own playlists (e.g "My Discovery"). This way you can build it up every week.
Mine currently has 150 songs from the last 5 weeks of Discovery - great for shuffle play!
I was one of the people who moaned at Spotify for taking away the Discover Weekly playlist a few months ago. Now it is back let's not moan because we have simply forgot to save the songs!!! (otherwise they may take it away again!)
Let's just congratulate Spotify on giving us new unheard of music every Monday - I've found countless new artists/bands in the last month...
Think you misunderstand by what I mean as pointless...
People on this thread who forgot to save the discovery playlist are asking others to post the playlist up on here thinking it will contain their songs. But becuase it is unique it will only be the other persons songs....so someone liking folk may get death metal!
and yes, I think it would be good to automatically save (or maybe have a option in the settings for this).
While we don't have the robust capabilities of the desktop client, I did find one version fo play history in the mobile client that will help identify the artists, but not the tracks.
In iOS, hit the menu icon in the top left, once there click your profile at the bottom, that should at least bring up several recently played artists (these for some reason are not found on my recently played queue elsewhere in the app). While I did not find all of the recently played aritsts from last weeks playlist, a good deal of them were there.