I applied through a recruiter. I interviewed at Google
Interview
There was a pretty short phone screen that involved a Fermi estimation (eg, how many golf bus can you fit in a school bus?), and then a full day onsite scheduled.
The onsite interview was literally nothing but 6 hours of Fermi estimations with 5 different people. It was the worst interview I've ever been in, there was basically no discussion of the job, no "warming up" socializing, nothing but building models for Fermi estimations. Awful.
No discussion at any point about product design, analysis (outside of Fermi estimations), no questions about estimating market sizes or ROIs on product features, etc. Basically no discussion or questions about products or the product manager role.
By the end of the onsite I was pretty annoyed and told them this was the worst interview I'd ever been in, I suspect that had something to do with no getting an offer.
Interview questions [1]
Question 1
How many cars are on 101 between San Francisco and Mountain View? How many piano repairmen are there in the United States? How many golf balls can you fit inside of a school bus? How many people work for Google worldwide? How many computers does Google own?
Very self-driven, first of multiple rounds, where I had to take the initiative to arrive at the problem, constraints, approach, solutions, tradeoffs and reasoning behind it in a matter of 30 minutes.
You would have to do a hiring assessment first, then a recruiter screening follows. First round interview with the hiring manager. Majorly product sense and product improvement. The questions were not direct though.
Overall a lot of steps to the interview process. Talked to different people and had opportunities to ask questions. Many different stages which made it a lengthy process overall. Wasn't too bad.