Zoe Heriot is an astrophysicist and astrometricist first-class, pure-mathematics major with honors, from the twenty-first century. She met the Doctor and Jamie when they arrived on the Wheel, where she was working in the parapsychology library. Zoe helped them to defeat the Cybermen and then stowed away in the TARDIS. The Doctor made her watch "Evil of the Daleks" (well, basically) to be sure that she wouldn't be frightened by the things he tended to encounter, but this did not dissuade her.
With the possible exception of Romana, Zoe is the most intelligent companion ever to accompany the Doctor. Often compared to a living computer, Zoe possesses an astounding total recall of facts, and she is highly talented with mathematics, computers and logic. In fact, she once claimed that the Doctor was almost as clever as she was. She can do complex calculations very rapidly, and can send primitive computers into such a tizzy with insoluble equations that they blow themselves up!
In the City where she grew up, Zoe studied under a parapsychologist renowned for using brainwashing techniques which emphasized facts and figures at the cost of emotional detachment. Some of his pupils apparently never fully developed their emotions, and initially Zoe is rather lacking in emotions as well, but during her first adventure with the Doctor, Zoe realizes that logic and facts are not always enough. As her time on the Wheel is put further and further behind her, Zoe becomes much more in touch with her emotional side, even letting loose quite a few screams. Zoe begins to realize that relying on logic is not always the best course of action, and she starts trusting her intuition more. When danger threatens and the Doctor is nearby, Zoe gets practically jumpy, nervously waiting for him to do something. But she has a difficult time completely putting her logical nature behind her, especially when she is asked to disbelieve something that she can clearly see in front of her.
Yet when she is on her own, without the Doctor or Jamie to cling to, Zoe is a mostly implacable person. She is never ruffled by megalomaniacs or authority figures, much less anyone else. Instead, she uses logical thinking and determination to see her through sticky situations. And maybe a little bit of judo, if she sees the need. Zoe also appears to have had some medical training.
Zoe is often described as 'elfin', meaning that she is short and very slender. She has a bob of dark brown hair and blue eyes. Zoe tends to wear futuristic clothing, such as a glittery silver catsuit or a scallop-edged PVC jacket and skirt.
When the Doctor was forced to summon the aid of the Time Lords in order to capture a dangerous criminal, the Time Lords used the opportunity to punish him for his own crimes. When he was forcibly regenerated, both Zoe and Jamie were sent back to their own times, with the memories of their adventures with the Doctor erased. It is possible that, in the future, the Doctor returned to visit Zoe and restored her memories.