I applied through university. The process took 2 days. I interviewed at Princeton University (Princeton, NJ) in Jan 2012
Interview
Lengthy application, interview was quick (one weekend). Mostly about touring the place rather than a rigorous interview. Mostly the interview weekend functions to screen out the wackos who look good on paper. Once you get the interview you are more or less in.
I only had to send an online submission - no interview via phone or in-person was required so I had to compile a detailed CV, cover letter and writing sample
I applied in-person. The process took 2 days. I interviewed at Princeton University (Princeton, NJ)
Interview
Interview with several faculty members one on one. They talked to me about my research experience and where I wanted to take my own work. They also described their work and solicited my thoughts on it.
I applied online. The process took 2 months. I interviewed at Princeton University (Princeton, NJ) in Oct 2012
Interview
There's just an online application. This application involves writing a personal statement, providing letters of recommendation, submitting all of your transcripts, and, finally, submitting your GRE and GRE Subject test scores.