Alright, let's get the obvious out the way. She's got a fantastic behind. But if that's all you know of her, you're missing a whole lot.
She's smarter than the Doctor, been raised as a prodigy, and can blow up a computer with her mind. Along with a Scottish guy (who really was the odd man out if you think about it), and BASED TROUGHTON, she went across time and space, facing down people with a weird metal modification fetish, an old man who tried to make them play with children's characters, and...the Krotons. Whatever happened to those guys?
Anyway, eventually they accidentally got in the way of a giant historical LARP Fight Club, and BASED TROUGHTON had to call his parents to bail them out. They roofied Zoe, and she was swiftly returned to the Wheel. Oh wait, did I mention the Wheel above? Who cares, everybody's only here for Zoebutt anyway.
She screamed a lot and wore a sparkly catsuit because she was from the future of course, just like we all wear today.