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.
I applied online. The process took 1 day. I interviewed at Jane Street in Jan 2017
Interview
Applied through website and received a prompt response via email. Scheduled a phone interview for following week. They called almost on time (about 15 mins late) and asked some probability questions. I had trouble understanding the interviewer's accent. He was helpful but I was nervous and only got through 2 problems.
Interview questions [1]
Question 1
You have a shuffled deck of 26 red and 26 black cards. You play a game by repeatedly looking at the top card and either discarding it or ending the game. At the end if the color of the next card matches that of the top card you win, otherwise you lose. What is the optimal strategy?
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.