I had an unconventional interview process in that I had not originally applied for graduate school at Dartmouth, but happened to find myself talking to some of the professors. The encouraged me to apply, I was accepted, and that was that. Dartmouth is excellent in that it is a small enough school that individual professors and students can have a big impact on the department, and the upper management has a lot of faith in the professors. Typically, however, the application process consists of making contact with a professor and asking if the are accepting graduate students. This is a critical first step to applying to graduate school. Next, you fill out the online paperwork and send transcripts, etc. If they like you, they will offer you an interview. For the interview, you are flown to Hanover, where there is a recruitment weekend. The recruitment consists of giving a presentation in front of the department, seeing presentations by other applicants and professors (asking questions during these talks is an easy way to make yourself stand out). You will also meet with individual professors at some point. Basically it is a weekend to feel scrutinized, in competition with your peers, and stressed out in general. After that you go home, wait a few weeks and hope to hear from them.