I applied online. The process took 1 week. I interviewed at Jane Street in Jan 2016
Interview
Applied online and heard back by email with in 2 days. Set up phone interview. Scheduled for 40 mins but it took longer. Interviewer was very nice. He was willing to answer questions at the end even though it already took over 1 hour and 20 mins. Questions were based on probability and statistics. To be honest I did not prepare well so I had a hard time making progress on the problems. Definitely would recommend to apply though.
Interview questions [1]
Question 1
Typical questions found in quantitative trading interview books.
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.