I applied online for an embedded analyst position (title is set to change I am told). I received an email almost 2 weeks later that they'd like to have a phone interview. That was set up a few days later. I spoke for 30+ minutes to, I believe, an engineer who asked me some basic resume review questions and began to broach some more technical items- which I believe were probably very elementary for people with CS backgrounds but, for me, were not so easy. When I got off the phone, I figured that was the end of my Palantir process but I sent a thank you email to the recruiter the next day and received an invite for an in-person interview which would be two weeks later. The interview process consisted of 5 x 45 minute interviews, all one-on-one and back-to-back. Normal interview questions, reviewing your previous experience, how you would engage customers, how you would problem solve. Also a few brain teasers which were in the normal range for difficulty, and mostly just wanted to see your thought processes in action, I believe. They called me the following Monday to let me know I did not get the job. I am happy I interviewed with Palantir, I felt that they were fair and friendly. And their expectations were pretty transparent too. I left the interviews feeling not up-to-par with my technical skills and that is, I believe, what killed my chances. My advice: if you are applying as an embedded analyst/business development side, analytical background is required but so is a healthy dose of technical know-how, in fact a robust technical skill set is required.

Phone interview -> in person interview -> in person interview -> founder interview. Standard non-programmer tech questions. Less focus on brain teasers and more focus on reading and understanding data (they brought in papers with charts for me to read and interpret). The (last) founder interview actually has a fairly low pass through rate, so don't think that meeting the founder = offer. Only problem was entire process lasted a few months for me - you need to stay on top of the recruiting department (through your referrer most likely) to keep the process moving quickly.