I was called by one of their recruiters after a friend referred my resume onward, and then began a series of three phone screens with people in various Technical Program Manager roles across the company to get a feel for me, my personality and if I'd be a good cultural fit for the company. The interview questions were mostly about projects I've managed in the past, examples of things that I designed/managed that went really well and those that didn't, and one of the interviews had me analyze a current Amazon product or service for its strengths and weaknesses. Next, I needed to submit a writing sample to them answering one of two questions about challenges I've had in the past and how I solved them.
Once that was in, I was invited to fly to Seattle and interview in-person with six different managers and senior managers. The interviews ranged from discussions on managing teams, how would I solve technical problems that Amazon has encountered, and a few design questions both real-world to Amazon and more esoteric in nature where I would whiteboard a solution. Everyone I spoke to seemed to radiate about the company and the culture there, whilst noting that the biggest problem is finding the right talent and the rush to find and hire the right people fast enough.