First interview was a 30 minute on-campus interview. During the first minute or so, the interviewer asked me a few questions about my resume. It seemed as if he wasn't really interested in the answers, and that he was only asking these questions to break the ice. He then proceeded onto some math questions. The first two or three questions were pretty easy, but I ended up being stumped by the last question and was not able to finish it with only a few minutes left. I thought I had failed, but later that week I learned that I had proceeded to the second round. I had two more phone interviews after the initial on-campus interview.
The interviews consist of mathematical brain-teasers. They say that the interviews will only last half an hour, but in my experience, if you're doing well so far, the interviewer will ask you more questions and let you have more time. This was my experience with my first phone interview, which lasted about 45 minutes. In my second phone interview, after some initial talk about my resume, I got stumped on the first question. After about 20 minutes passed, the interviewer gave up and asked me a second, much easier question which I was able to answer. She then promptly ended the interview.
Based on my experience, it seems that in order to progress with Jane Street, you simply need to be able to answer all questions asked of you, with the exception of maybe the last question asked in a particular interview when you are running out of time (like I said, during my first interview I was stumped on the last question; on my second interview I was running out of time and gave an answer to the last question that was close, but not correct, but I still progressed to the third interview). I've heard of people having as many as four or five interviews before a final on-site interview. If you're one of the few who survives through all the rounds, then you're probably pretty bright, and they will offer you a job.
Even though I messed up, I thought the interviews were pretty fun. The interview questions are pretty cool. They're also not incredibly hard, but if you don't attack a certain problem the right way, you can easily get stuck.
One other thing - at least at the stage I managed to get to, they don't care if you have any experience with or knowledge of finance or programming. They only care about how smart you are.
