Earlier quoted context omitted.
Discover weekly is the reason that I pay for Spotify. I'm an old guy that prefers vinyl to mp3s, misses the local record store terribly and hates radio, so modern music distribution sucks for me. I first tried Spotify many years ago, back when playlists were quite new. At the time, I was living in the UK and a big user of last.fm but, out of curiosity, I spent an afternoon building one playlist out of the few tracks…
Funnily enough, Discover Weekly almost never works for me. I like the overall service Spotify provides, but the discovery features don't really cut it for me. As an example, I usually don't really like most music that goes into the house, techno, electronica or even dubstep directions. Most songs I find to be horribly repetitive and lacking in good buildup/melodies. However, there are exceptions I can enjoy very well…
I suspect this uses the same underlying algorithms as Discovery Weekly, except that DW uses the songs you've listened to as the basis.
Discover Weekly does suffer from a pollution problem — listen to one style of music for a while, and the entire tone of your DW playlist will change. Fortunately, the above trick works.
There's also the Release Radar [1] playlist, which seems to be an undocumented feature. It gives you new tracks by artists you follow, as well as related artists based on some mysterious metric.
DW explicitly excludes classical music and also jazz, for some reason. I think I've had Arvo Pärt come up, probably because he's a contemporary artist; same with folks like Max Richter and Jóhann Jóhannsson.
[1] https://open.spotify.com/user/spotify/playlist/37i9dQZEVXbtE...