0) Before the interview with Klarna you had to go through a one hour interview with some kind of external recruiting agency. These are the usual guys. They do not know that much about you or what the company want except of what they have been given. If you just read the homepage and state that you consider their values likeable and what they have accomplished given their short period of time you have a fit. They consider themselves a start-up and everything should happen quickly. Think Google, Apple, Spotify, Uber and a bunch of companies at techcrunch and they would like you. Make sure to get the general idea right instead of namedropping. Even though this is how Klarna wants to seem themselves it is not always obvious that the interviewer from the external recruiting agency are into start-ups and payments.
1) Two tests online: one numerical and was about understanding the content of a text. Pretty standard by other means. The numerical was about being able to calculate gross profit, various financial numbers related to the P&L quickly based on some data etc. and how much a water etc. different objects could contain. The amount of calculations required and the amount of time given were pretty normal to what you would expect from a second degree consulting firm such as PwC.
2) One 1.5 hour interview containing a 30 min market size estimation type of problem and then 1 hour of behavioural fit questions. Before that you had to do a pretty simple IQ test at the office, 20 questions in 20 minutes if I remember correctly.
3) The last part consisted of a 60 min interview with one of the high-level managers.