I applied online. The process took 1 week. I interviewed at Jane Street (New York, NY) in Jan 2016
Interview
The interview was just two questions related to probability and math. The interviewer was extremely friendly and helpful in answering questions. Still waiting to hear back, but it was very fun as the questions were challenging but enjoyable.
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.