I was first contacted by Palantir via a recruiter (Oxford Knight), who were themselves a pleasure to work with. I had a series of emails and a GTKY-type Skype call with the recruiter, followed by a technical screen (again over Skype) from a Palantir engineer, in which he asked some basic algorithms questions (mostly over the design and use of hashmaps).
Apparently I passed that, as they then flew me out to Abu Dhabi (where the role was located), where I met the (very small!) on-site team and had an afternoon with 4 interviews. Two of these were technical, algorithms-type conversations; the other two were more social chats about technology in general and some of the work I'd done recently (Ph.D. research and iOS development).
Before leaving Abu Dhabi I got another phone call from the recruiter, arranging a second on-site interview in Palo Alto. I flew to California the next week for a similar round of interviews; these were (much) more technical in nature. After three tough algorithms-type interviews conducted by a rotating mix of interviews (some of which were silent observers, and some of which were remote and conducting the interview via Skype video) I had a VERY BRIEF and VERY STRESSFUL interview with one of the founders of the company. He stressed that he had very little time to spend on our interview (as he had dozens to get through that day), and rapid fired extremely perceptive questions about my Ph.D. research and some complex algorithms (heaps, mostly).
This was actually a tougher interview than my Ph.D. defence.
A few weeks later I received a (very generous, comprehensive) offer from Palantir for a FDE position in Abu Dhabi, which I deferred. Great company, great people, interesting interview process -- but the role was in a truly terrible location.