First interview was a phone screening with a SpaceX recruiter. We went back and forth a few times before I was contacted by a SET for a technical screening. The 30 min technical screening consisted of an overview of the position/team, a review of my past experience, and a handful of technical questions. I was contacted a week later for a 3-hour technical screening, which consisted of building part of a game with different players and how to calculate who will win if they battle each other. This part was pretty fun, and I was able to send in my code periodically to get it tested and get feedback from the SET.
Overall, a very positive experience. SpaceX is a great company and it is doing great things. It's filled with brilliant people, and I highly recommend applying.