I applied online. The process took 6 weeks. I interviewed at American Express in Oct 2012
Interview
HR does initial screen. Hiring leader does second screen. Then you meet a couple of his colleagues that you'd work with most or that he/she respects most. Then you meet his boss. Then you meet his boss' boss for final interview. So that's 5 interviews to get one job. It's a long road so be patient and persistent and prepared. They'll ask you to tell you about your background, what skills are transferrable to job, previous experiences that relevant to job, what you'd do if hired, what the biggest challenges are, etc...
Interview questions [1]
Question 1
What is the biggest challenge facing this biz unit? If it's so challenging, why do you want to work here?
Amex focuses a lot on the ability to drive results and its culture. Make sure you know its Blue Box Values and know that you'll run into situational questions that you should address in a SAR format (state situation, what was the action taken and what results resulted)