I applied through university. The process took 1 day. I interviewed at Two Sigma
Interview
They flew me out and put me up in a hotel. The day of the interview I had one hour-long interview with two hiring people (who apparently also teach a poker class for interns). In addition, I sat on the trading floor and watched someone trade for an hour or so. They then talked to me about whether or not I wanted the job, what concerns I had, etc.
Interview questions [1]
Question 1
Nothing was difficult. They asked really basic probability questions. The one that was the most difficult: If the probability of seeing a shooting star over the course of an hour is .64, what is the probability of seeing a shooting star over the course of a half hour?