After application, it was 2-3 weeks before hearing back from the team lead (not HR, for which I was glad) about setting up a phone interview. We set one up and discussed my background, resume, education, and general interview stuff: how do you prefer to think, etc. At the conclusion, the interviewer said he would like to set up another phone interview with another member of the team, and I sent available times. The second interview was more focused on the company itself, and what the particular development team (the one I would be joining) did.
Another two or so weeks passed before I received a message from the team lead, saying I'd moved forward to the written analytical test. It was sent to me by email on a mutually discussed and agreed-upon date/time, and I completed it at home, scanned my on-paper answers into a PDF, and sent it back to him. In a few days, I was informed I'd moved to the in-person interview.
The in-person interview was three parts, and each involved interviews with members of the team (again, I was thankful for minimal HR intrusion). One interviewer was the team lead again, with a mix of analytical and "soft skills" questions. The second was more technical and mathematical, getting further into the statistical and calculus elements of the position. The third was mostly personality- and behavior-based in the questioning.
I was told I'd hear back within two weeks, and I did. The interview was a Friday; I heard back in 13 days precisely. Unfortunately, I was not selected, but it was a very nice process overall. I even inquired to the team lead if there was anything in particular that made the chosen candidate, and he was kind enough to tell me what made the difference.