SpaceX Interview process is separated into three sections
1) Technical Recruiter Phone Screening for about 30 minutes. Going over resume and touching on technical aspects. The prompt is "Please be sure to take the call in a quiet area with good reception. We recommend you prepare to discuss in detail your employment history, professional/technical achievements, and motivation for wanting to join SpaceX"
2) Team Member Technical Interview for about 45 min - 1 hr. Going through a series of questions to check technical understanding. The member I spoke with is the Team Leader and he helped guide and hint toward answers. The prompt is "Please be sure to take the call in a quiet area with good reception. We recommend you prepare to discuss in detail your employment history, professional/technical achievements, and work style. If you would like to provide examples of your work for the hiring team prior to the call, please feel free to send those to me and I will forward as appropriate." However, it was almost all engineering and mathematical concepts related questions.
3) Onsite tour, technical presentation on a project you have worked on, and a hot-set interviews / 1-on-1s with team members and leaders.