I applied to the company through their website, completed a personality assessment online, and was contacted approximately one week later that they were interested. A phone call was set up with a representative to further discuss the role I applied for/to bring up other roles that I would be a good fit for. The representative got in touch with recruiting, and they set up testing on my university's campus for the various roles I was being considered for. The test for me consisted of math/logic questions, programming questions, and picking up on a new programming language's syntax.
A few weeks later, I was contacted with an invitation to interview on site, which consisted of a one night stay in Madison. There was an option to do dinner and a tour of Madison the day I arrived, so I could explore and see if the area is a good fit for me. The following day started at 8:30 (start time varies based on how many positions you are interviewing for). I met with my recruiter briefly, then went to a Q&A session, a brief tour, and a demo session to see the products developed at Epic. My first interview (the only one related to the reporting engineer position) was allocated 45 minutes. It was incredibly laid back, and I don't remember being asked any majorly technical questions. Everything was focused on my past work experiences.
You get to eat lunch on campus for free, and there are snacks/drinks out in lounges for candidates.
At the end of the day, I met with my recruiter and was asked some very HR-ish questions. Things like why Epic. I had another job offer with a deadline, so I brought it up. Turn around for the offer was incredibly quick; I was contacted less than 24 hours after leaving.
Notes: If you are offered an on site interview, do not dress up for it (unless you're going for management or something). You'll be told to dress casually, and the employees follow suit. Also, if you have time to kill before your flight, ask the reception desk for self guided tour packets of the two campuses; they're incredibly interesting!