I was contacted by one of Postmates' in house recruiters. After missing our first scheduled phone call (which she apologized profusely for), the interview process was smooth and on time.
There was an initial phone screen via Skype which consisted of programming trivia questions. Next I was scheduled for a full day interview, five hour long sessions plus catered lunch with a couple of other engineers. I arrived early and waited a few minutes for the recruiter to meet me. The receptionist kindly brought me coffee. The recruiter took me on a short tour of their new office, pointing out various amenities (game room, lunch room, kitchen with beverages and snacks, etc).
I spent most of the day in the same conference room. My interviewers were all on time, friendly and did their best to answer my questions. The interview was more focused on actual coding than white-boarding. The interview sessions consisted of debugging an app, designing and implementing an algorithm, writing a small program from scratch, designing a system and API (on the white-board), and a talk with the new VP of engineering. I felt that the problems were fair and thorough and I left with a good opinion of the quality of the engineers.
The recruiter called me a couple of days later to tell me that Postmates had declined. She gave me pretty detailed feedback, with the key reason being that I wasn't enthusiastic enough about the company. (This primarily via the VP of engineering.)
I wasn't super-disappointed since the feedback was pretty on the mark -- I have my doubts about the long term prospects of Postmates or any of the various on-demand/delivery start-ups.