Process took about 6 weeks. Applied online with only my resume. Received a phone call from a recruiter and they passed my resume around and I was being considered for multiple positions on the production side. First phone call was with the recruiter and they asked basic questions - nothing technical. I think that they just wanted to know if you fitted the basic qualifications and if you were enthusiastic about SpaceX. The phone call lasted about 30 minutes.
Afterwards, I had phone interviews with different departments and they asked questions more specific about my role at my current employer - again 30 minute calls. The major questions were if you did something significant and the technical aspect of it (i.e. statistical information, issues you have had and how you solved them, what was your role?).
Got called in for the presentation - which was about a project you worked on and a major problem that you solved and your thought process. Afterwards, went to the one-on-one interviews. Again, asking questions about problems you have solved and more industry specific questions. I thought I was a good fit, but it didn't work out, I'm going to definitely try again.