The different stages have been described by many others before me, and you'll be reminded of them countless times by the recruiter, so no need for me to describe them here. The process is quite structured, which is good because you know exactly what to expect and how you are being evaluated. The interviewers seem quite nice and want to help you succeed, and the recruiter gives you very detailed feedback after each round.
What matters really in the end is how you solve their business cases, that you show adaptability and are able to come up with concrete, quantitative solutions.
The most disappointing thing to me was that it took them 3 months to take me from first contact to final interview, with several weeks in between each phase of the interview... And in the end I was rejected, so it was extra disappointing... I think if this is the usual process, Booking.com will lose many great candidates, who get an offer by another company way sooner...
Additionally, for me personally, this type of interview is not very suited to my way of thinking and processing information. You have to solve a completely new problem on the spot (actually, at least 5 different ones), and while doing that you have to be constantly saying your thoughts out loud. I did OK, but not my best. I just could not think and talk at the same time, so sometimes I would stop to think for a bit, and I was later told that this was seen negatively in my evaluation... I am of the opinion that Booking.com should evaluate the ability to solve business cases a bit differently, as talking while thinking is a requirement to do a good job as a data scientist.