I applied through an employee referral. The process took 6 days. I interviewed at SpaceX (Hawthorne, CA) in Mar 2016
Interview
Basically they do a phone interview first. This is typically with an engineer rather than management. then when they finish the review, which included several technical and challenging questions, they'll move on to the next phase, which is a phone interview with management. This is even tougher, with more technical questions and more personal questions as well. It's super friendly though.
Interview questions [1]
Question 1
What about SpaceX's goal's do you most identify with and why?