Exxon organized interviews through my university. The interview lasted about 45 minutes and went through a variety of questions. Questions were broken down into a few different catagories: Leadership, Teamwork, Problem-Solving, Communication, Character, etc.
The person interviewing me was not some random HR rep, but an actual engineer working at the company who knew the types of things that I was talking about. It was very refreshing.
At the end of the interview, I was told that my name would be added to a database of candidates, and that hiring managers around the company would be given the opportunity to search the database for people who fit the positions they were trying to fill. After about a week, I got a call back from a separate hiring manager who scheduled a second phone interview with team leaders of a specific group. Finally, after about a week, I was asked to travel to the campus to do an on-site interview.
The on-site interview was a whirlwind: After giving an hour presentation on my research, I was moved between 7-8 different members and managers of the group to have 45 minute interviews. All of them were similar to the original one that I had received at my university and the phone interview.
After about 3 weeks, I was given an offer.