Following a departmental email, I sent my details and CV to the person coordinating the hire. I Was contacted a few days later to let me know my application was in and that they'll schedule a phone screen in a few days, which they did (via email). The phone screen was fairly general and non-technical, "what type of work you've done in the past, what type of work do you prefer doing" type of questions. After the screen, I was contacted via email and an on-site half-day of interviews was scheduled (I live in driving distance of Apple offices). The interviews were half-technical (mostly data structures and algorithms questions, some general machine learning knowledge questions) and half-"touchy-feely" (what's the project you've done that you like the most, and why, why Apple, etc.). As of a week ago I've been told the hiring process is still ongoing and I am waiting for their final word.

1 screening interview, 2 technical interviews. Fairly easy, the interviewers were very kind and helped through the process. The questions were related to my field of research and their project.