I applied online. The process took 2 weeks. I interviewed at Jane Street in Apr 2016
Interview
Asked some difficult brain-teaser type questions. 30 min phone calls per round, I made it to round 2 before getting the rejection. The interviewers were friendly and were able to give hints and clues (though I suspect that if you needed help this would reduce your chances of employment significantly). Overall an interesting interview process, but definitely very stressful.
Interview questions [1]
Question 1
You have a number, and the product of its digits is 96. None of the digits is 1. What is the largest and smallest number you can think of?
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.