I applied through university. The process took 2 weeks. I interviewed at Jane Street in Nov 2015
Interview
I applied through my university's career fair by giving them my resume, and received an email within a week from a recruiter asking for an interview. My interview was postponed last minute (i.e. 5 minutes after it was supposed to have started) because they were apparently really busy that day. I was told this by a different recruiter, neither of whom interviewed me. My interview was with a trader. He asked me a bunch of hard mental maths and probability questions, but I messed up due to rust.
Interview questions [1]
Question 1
Two dice. One 10-sided, one 6-sided. Guess a number between 2 and 16, if the sum of the dice shows that number, you get that number of dollars. What is the best number to guess to maximise winnings?
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.