In total, 6 interviews. After an initial Skype interview with my future manager, I was invited to Berlin for a round of four more in-person interviews. All travel and hotel expenses were paid for. The hotel was top-notch and right across the street, which made the experience very smooth as I did not have to worry about public transportation, traffic or getting lost. I had one more Skype interview with someone based in California after my trip to Berlin.
The interviews went great. I was part of a conversation rather than being grilled and lots of effort went into making sure we were the right match for each other. My advice: come prepared. Know the company, the industry, anticipate the problems you're going to be facing and show that you already have some ideas about how they could be solved.