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.
For the undergraduate summer analyst internship.
Applied in late October and got a phone call before Thanksgiving holiday for the first round phone interview. The process was expected, as described by other comments. Three questions, mind teasers. Thought I messed up with the easiest one.... Got rejected after a week.
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.
J'ai passé un entretien chez Jane Street (Londres, Angleterre)
Entretien
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.