I applied online (without any referrals) and got a call back two weeks later. The process lasted three to four weeks for me and included several phone interviews and a writing test before the in person interviews. The writing test was extensive and needed to be finished before the in person interview.
Amazon does take care of you during the process (travel, expenses). They have a whole department that takes care of this! The actual interviews are quite challenging. I spoke with 6 different people during the in-person interviews (almost 45mins to an hour each) including a lunch interview. One thing I found interesting was that the interviewers barely make eye contact with you during the interview because they need to fill out a comprehensive STAR form with all your answers.
At times, it felt like they were trying to trick you just to see how you'd react, especially when they'd bring someone in from a completely different department to test you. This style of interviewing can be exciting for some and I'm guessing that's how they weed out people that don't fit their culture.
The entire interviewing process at Amazon seems like a machine. The recruiter I had been first speaking to had left her job mid-way through my process and another. Overall, it seems like employees are constantly having to interview candidates.