I applied through college or university. The process took 4 weeks. I interviewed at Capital One in Feb 2015
Interview
I applied through my school's internal career portal, and included a resume and cover letter. They contacted me to schedule an interview, and the first round was on campus. The first round was a 45 minute case interview, and that's literally all it was. There was no time to discuss anything except the case. The case wasn't too hard (or at least it was easier than the one on the website). I didn't do all that well on it - I made a few little mistakes along the way and probably took too long coming up with some of the answers. I didn't explain how I arrived at my conclusions too well either. I did, however, solve the case in the end. Overall the process was kind of dry and mechanical, and the interview and application process did not let me get a feel for the organization at all.
Best interview I've had in my hunt for internships. They make you feel like they want you to succeed and they really do. By the time you get to the campus interview you already are qualified, it's just making sure you didn't get lucky with the qualifications and that you are someone they'd like to work with(good personality). At least that's what I think it was all about.
I applied online. The process took 2 weeks. I interviewed at Capital One in May 2013
Interview
Phone interview first, asked some basic statistics questions including probability and linear regression.
On-site interview contains behavioral questions, role-play, and case study parts.