I applied through college or university. I interviewed at Jane Street
Interview
First round was a a short 30 - 45 minute phone call with some basic probability questions. None of them were particularly tricky and it seemed to be more of a "do you know the basics?" with them also asking for what assumptions I was making and why. The second round was two questions which I found much more challenging and was allowed one hour for. For both they were willing to work with you and wanted to hear your thoughts out loud. They let me run with a mistake until I noticed it and then would go back to point out where I went wrong.
Interview questions [1]
Question 1
Which of the following gives you the highest expected value: the square of a singular die roll, the product of two dice, or the square of the median of three dice roll?
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.