Called in for an interview two weeks after submission (varies by department of course, CU is huge!). The lady was very nice (again, interviewer will vary by department), told me what the job entailed and asked me to tell her a bit about myself. Very relaxed interview. Found out I was hired a few days later - the HR department was a nightmare (took me weeks to get paid because I'm international apparently!).
Columbia University overall is a great place to work, however the departments are very "separate" and non-solidified so getting through the red tape takes forever.