I applied through an employee referral. The process took 1+ week. I interviewed at Tesla in Apr 2016
Interview
Was given a "take-home" style programming test. Answered a few smaller programming questions and had to create a small application sample to demonstrate what I could do. Not a simple thing either, this application sample easily took half of a weekend. This was reviewed by a manager, who decided if it was good enough to proceed to a phone screening/interview. The call involved a discussion of the position and what the team does at Tesla, my history and experience, and eventually finished with another programming quiz on a shared coding site. A second, similar phone interview with another manager on the team occurred a couple days later.
Interview questions [1]
Question 1
They didn't actually ask much outside of general programming and algorithm knowledge, the interview was more a conversation about everything the team for this position does.