Once you apply online, they do a Skype panel interview with you and current fellows (first and second years), which took about 20-25 minutes.
If selected, they invite you to on-site interviews. They invite you and other candidates to dine with past/current fellows and the fellowship coordinator. Then, the next day is a marathon. It consists of a) presentations by leadership & tour of the hospital, b) case-interview type question, and c) panel-interview with 10-15 people from management & leadership.