I applied online. The process took 3 months. I interviewed at Tesla in Apr 2014
Interview
The process can either be extremely long or extremely short. It depends on when you are about to start summer break. I applied really early and didn't get noticed until close to finals. After that the process became expedited. The normal sequence for me was:
1. General HR interview
2. Initial team interview
3. Technical team interview
4. Repeat 2 and 3 for how ever many teams are interested
In total I had about 5 interviews since more than one group was interested.
Interview questions [1]
Question 1
What was your biggest engineering challenge in college?
Some teams asked incredibly specific engineering questions, some were much easier (i.e. bending stress vs. general CAD experience)