I applied online. The process took 6 weeks. I interviewed at American Express (New York, NY) in Sep 2013
Interview
I had two phone calls and then was brought in for a day of interviews. Overall, very pleasant. Most of the questions were aimed at demonstrating how I would think through a problem. Not full of technical details, but rather pseudo-process/code. Amex is very culture conscious, so if you can demonstrate that you are someone who is a problems solver, and you're pleasant to work with, it shouldn't be a difficult interview.
Interview questions [1]
Question 1
How would you identify someone's favorite spot using card transactions?