Zappo's internship interview has been explained multiple times on the previous reviews:
After passing the resume screening you go through a two part first step.
One part is the challenge. It varies with the role you are applying for. For the Product Management Intern role it consisted on coming up with a new product for Zappos, talking about the value proposition, the target market and the overall business model as well as making a prototype.
Another part is a virtual interview in which you are presented with questions, have time to think (30 sec) and then 1 to 2 minutes to answer, while being recorded via webcam. They are mostly behavioral questions to see if you are a match for the company. Some easy technical questions related to the position can also be expected.
I wasn't selected for the next part of the interview, so I can't talk much about that.