Martha Jones is a Female Human who worked as a medical student at the Royal Hope Hospital in London.
The twenty-three-year-old Martha was working at the hospital when she encountered the Doctor, and later joined him as his companion on his adventures. The Doctor insisted, however, that he had not brought Martha aboard the TARDIS as a replacement for his previous companion, Rose Tyler. (DW: Smith and Jones)
Family
Before she met with the Doctor, her parents had split up, and her brother's girlfriend had his baby. When she met the Doctor, it was her brother's 21st birthday. Her cousin, Adeola Oshodi, used to work for Torchwood 1. (DW: Smith and Jones)
Alongside the Doctor
Martha Jones first met the Doctor in the street on the way to work; she had been on the phone to several members of her family when she bumped into him. He took off his tie, saying "Like so! You see?" before getting on his way. She looked momentarily confused before making her way to her work: she was a medical student at the Royal Hope Hospital in London. As she entered the building, she saw two men appearing like motorcycle couriers, and, soon after, whilst taking her jacket from her locker, she received a strong burst of static electricity.
Then, Martha was one of those present to review the Doctor's case. She examined him using a stethoscope and was shocked to discover that he has two hearts, although she didn't say anything to anyone else about it.
She helped him defeat the Plasmavore "Florence" when the hospital was transported to the Moon by the Judoon, and later joined him on his travels. Her first meeting tuned out to be a way for him to prove that he could use his TARDIS to travel through time as well as space. (DW: Smith and Jones)
Originally she was frightened of the effects that may occur from traveling through time, although the Doctor's apparent confusion over the matter later convinced her that it was not easy to change history. (DW: The Shakespeare Code)
Time away from the Doctor
Martha spent a year travelling the Earth speaking of the Doctor whilst the Master ruled over them with the Toclafane. As a result of the destruction of the Master's Paradox Machine, only Martha and her family remembered that year spent with the Master. She decided she wanted to go and complete her medical studies, but gave the Doctor her phone; saying that she might want to return to travelling with him in the future. (DW: Last of the Time Lords)
Future of Martha
The BBC has anounced That Martha will Appear in Torchwood and become a member of Torchwood 3 For 3 Epsiode's. This will be When she is away from The Doctor in between 2008 and 2009. She will appear as a Companion In Series 4 in episode's 6 or 7 with another companion that the Doctor will pick up.