Applied as usual via their site, and got an automated response. A few weeks later I got sent a generic email asking me to complete a psychometric test and an aptitude test, which I did. The tests show you the results, and apparently I'm really clever as I was above average on the aptitude stuff (it was all the usual basic puzzles, sequences etc) and the psych thing spewed out some rubbish as well.
It seems that they take the psych test seriously, as (over a month later) I got another generic email letting me down gently (with the usual laziness of "We have so many applications to deal with that we can't spend 30 seconds explaining our reasons").
Seeing as psychometric tests are no more use than horoscopes, or "Which Harry Potter house do you belong in" tests, I was really surprised that somewhere that I'd presume to be as seemingly modern and progressive as Spotify would actually put any faith into them (they clearly liked my CV, and I did well on the aptitude stuff, and they hadn't bothered to actually talk to me 1 to 1 at any point, so it must've been based on that).
So in the end, a bit of a waste of time, although I guess I now know I don't want to work there...