I applied online. The process took 4 weeks. I interviewed at Jane Street (London, England) in Apr 2015
Interview
Phone interview. I was asked a series of mathematical and probability questions. It is important to know that they will ask you to bet on how likely the previous answers to your questions are of being correct. They can also ask you to do mental calculations in you head. Overall the interviewer was quite nice, they just want to see how you think. It is very important that you answer the questions as fast as possible, since they are looking for speed.
They tend to examine the logical thinkers that can communicate clearly and concisely, and some problem-solving exercises intended to explore how you gather and apply new information, very different from other tech companies' interviews.
Initial application and online assessment. Had a first round behavioral interview where they asked me about myself, my experiences, and a couple of brain teasers. The interviewer was very nice.
Phone interviews (at least 3) - questions were of mixed difficulty (some pretty hard) but the interviewers were friendly and they gave helpful hints. Kind of fun - review probability and game-type questions.