In "The Wheel in Space", Zoe aids the Doctor and Jamie in defeating the Cybermen and then stows away aboard the TARDIS. Zoe is a different kind of companion, not just an airhead screamer, she's a mathematical genius, although she still gets into a good bit of trouble, so maybe she's a mathematical genius screamer!
Zoe stays with the Doctor until "The War Games" story when the Time Lords put the doctor on trial. Jamie and Zoe have their memories of the doctor removed and are returned to their original times.
Zoe is played by Wendy Padbury.