I applied online. The process took 2 weeks. I interviewed at Jane Street
Interview
Applied online then had a phone interview. The application was fairly general at the beginning, sending off a CV. Then they asked for a phone interview, and sent over a document on probability and markets to read in preparation for the interview (although I don't think it was hugely relevant to the actual interview.)
Interview questions [1]
Question 1
Sum all the odd numbers between 1 and 100.
Then there were lots of probability based questions, lots using conditional probability. The difficult thing I found is that I was asked not to use paper and pen.
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.