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
Martha's mother is Francine Jones and her father is Clive Jones. She has an older sister, Letitia "Tish" Jones and a younger brother, Leo, who lives with his girlfriend and had a child. On the day that Martha first met the Doctor, her family had a row at her brother Leo's 21st birthday due to Clive insisting on bringing his young girlfriend Annalise, much to his estranged wife's disgust. The Jones parents eventually reconciled, after a year spent in captivity on the Master's fortress, the Valiant. (DW: Last of the Time Lords)
Martha's cousin, Adeola Oshodi, used to work for Torchwood 1 - she was killed when the Doctor overloaded the cyberman implant in her brain with his sonic screwdriver. (DW: Doomsday)
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)
After returning home in The Lazurus Experiment, the Doctor allowed her to stay on board the TARDIS. He gave her a mobile phone upgrade and a TARDIS key in the episode (DW:42)
Whilst travelling with the Doctor, Martha met several different species including, The Daleks, Catkind, The Macra, The Family of Blood and The Weeping Angels
Time away from the Doctor
When the Master took over earth Martha Pretented to make a weapon that would kill the Master She said that she had witnessed theToclafane Burn the islands of Japan. She spent a year on earth telling every one to think of the Doctor on a persific time so that the master could be defeated. This plan worked and the Master was shot by his wife Lucy Saxon. 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)
Joining UNIT and Torchwood 3
The Doctor gave a good word for Martha at Unit and she was asked by a woman if she wanted to join the organization and she agreed. She visited Torchwood 3 in Cardiff. She encountered a private medical organization called The Pharm. Torchwood sent her undercover but as she investigated it she was caught and the Mayflies were put into her body. Owen Harper saved her life using an alien surgical device but Alan Copley killed him. Just as he was about to shoot Martha he was shot in the head by Jack Harkness. (TW:Reset)
(WARNING: SPOILER ALERT)
Just as she was going to do an autospy on Owen Harper Jack stopped her. He had found the other resurection glove and used it to ressurect Owen. But also made a "death force" rise from Owen's conscience. This then attacked Martha and she aged to sixty years. The Torchwood team took her to a hospital and where she was told that she was going to die if this force was not destroyed. Owen destroyed it and which reversed the effects. (TW:Dead Man Walking) (More to come)