I applied online. The process took 3 weeks. I interviewed at Jane Street in Feb 2016
Interview
A series of phone interviews, where the questions were mathematical and based off different probability questions. The questions got increasingly harder with each successive interview and pen and paper was not always allowed.
Interview questions [1]
Question 1
Probability of 2 heads when tossing a fair coin five times
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.