I first got an invite to do a 30 phone interview with the hiring manager. The interviewer told me a bit about themselves and the position. They let me talk about my background briefly as well. The majority of the interview focused on asking technical questions.
I was selected to continue the process, and the next step was a 30 minute phone interview with HR. This interview was mainly straightforward generic HR questions (salary range, why do you want to work for Illumina, etc).
The last portion of the process was a panel series of interviews. I interviewed with about 8 people over the course of 5 or 6 hours. Each person had a different technical specialty, but all asked me technical questions.
Illumina's technical questions are very "Google-esque" in that they want insight into you think. You have to get creative to answer some in a way that reflects your background knowledge