Applied online to Insight Health Care. Submitted academic CV (they do not want a business resume) and personal experience story. The story is very specific - they want to know a time in which you influenced someone else and exactly what you did to smooth over a difficult situation. They're really looking for you to demonstrate four traits - problem solving, entrepreneurial drive, personal impact, and leadership.
Was called to have a phone interview. Very informal at first - the interviewer wanted to know about my background and why I was interested in consulting. Tried to weave my story together beforehand, which helped this come out more smoothly.
Transitioned into case portion. My only tip here would be to think out loud about your assumptions - my interviewed chimed in multiple times when I was missing something. I tried to be creative and show that I wasn't just regurgitating a framework.
Got an email the next week letting me know I was accepted into program.