I applied online. The process took 1 week. I interviewed at Jane Street (London, England) in Feb 2015
Interview
Good process, phone interview. Was very efficient on their end. Friendly interviewer, questions were hard but fun. All around a challenging interview, did not get an offer. Questions were solely technical on maths or probability or brainteasers.
Interview questions [1]
Question 1
We have a tricycle and we are going to travel on it for a thousand miles. We also have two spare tires with us. If you want each of them to be worn the same by the end of the journey, what is minimum number of stops you have to make in order to achieve this?
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.