My story is a bit different than most as I have two good friends of mine that already work for Progressive in a different city; however, the interview process is the same regardless.
I had been interested in working at Progressive after hearing rave reviews from my friends. After a job opening came available, I had one of said friends send me a link to apply as an employee referral. I lucked out in having a referral, paired with my extensive experience, at least guaranteed me to get through to step 1 of the interview process - online personality quiz and simple IQ test. The online testing was extremely easy in my opinion and I received confirmation that I passed within 2 hours of completion.
The next step involved a phone interview, which was scheduled to occur roughly a week after I took the online assessment. The phone interview was strictly "BEI" questions (BEHAVIORAL EVENT INTERVIEW)/S.T.A.R. questions. I was notified of this format ahead of time and it allowed me to prepare several scenarios that would fit many questions. (For those of you that have trouble with behavioral type interviews, I would recommend searching online for a list of common ones and writing out answers to them ahead of time in the S.T.A.R. format. By doing this, it will offer you great preparation for when the interview comes.)
At the conclusion of the phone interview, I was offered the opportunity to come in for a live interview and I was told I would be contacted by the local recruiter. About 2 hours later, I received a phone call regarding scheduling for the in-person interview. I "lucked out" and it just happened that they were doing interviewing the very next day with the regional manager (from what I heard, this is very atypical and usually the in person interview takes a week or two to get scheduled).
The next day, I went in for the in person interview at the local Progressive office. There were two interviewers - regional manager and another branch employee. The interview was more casual than other interviews I have been on in my life, with a section consisting of a casual chat about myself and the interviewers, then a more structured behavioral-based interview. There were roughly 5-6 behavioral questions and then some more small talk about my background and an opportunity to ask questions at the end.
Following the interview, I had to wait for Progressive's third-party background check company (HireRight) to conduct a THOROUGH background check. The process involves calling all past employers (if you've ever worked internationally, they will also contact these employers), your college/university for confirmation of your academic qualifications etc. As I had two employers overseas, and I had to give additional contact information to HireRight, the process was much more drawn out than the normal background check - about 2.5 weeks. (I think the process normally takes only a week or so.) I followed up to the interview by sending a thank you email to the regional manager (you can get this person's email by request from the regional recruiter that you're dealing with for scheduling).
Overall, I would say that while the interview process is extremely structured, it's no more difficult than the interview process of most other large companies that use the behavioral interview format. I highly stress preparing for the interview by searching the most common behavioral questions online and preparing detailed answers ahead of time. (If you write out the answers, you can even have the paper in front of you when you do the phone interview to refer to.)