Martha hooks up with the Doctor when the hospital they're in (She's a doctor too) is teleported to the moon with the TARDIS back on earth in an alley. The TARDIS never seems to be parked in places where it can enjoy the scenery. But they manage to get back, and the Doctor asks Martha if she'd like to take a trip. She's doubtful, but he tells her that he'll bring her back to the exact time and place she's in now. Yeah, right, Martha should have asked Tegan Jovanka about that. But, she decides to come along.
Martha stays with the Doctor until the "Last of the Time Lords" story where she saves the world. Figuring that she'd done her bit, she decides to go back to medical school and finish her degree.
Martha returns in "The Sontaran Stratagem" to ask for the Doctor's help, which he gives her, but at the end of "The Poison sky" when she's ready to go back to work at UNIT, the TARDIS slams the door on Martha, Donna, and the Doctor (Finally someone closes the door) and takes them to the planet where The Doctor's Daughter will be born. After they tidy up that situation, she finally does go home. Well, for a while anyway, she shows up for the Grand Finale of 2008, "The Stolen Earth" and "Journey's End."
In the "End of Time" story when the Doctor is taking his farewell tour of companions we find that Martha, sometime in the future, is married to Mickey, Rose's old boy friend. They decided to hyphenate and Martha Jones becomes Martha Smith-Jones. They're off happily fighting Sontarons when the Doctor rescues them from a Sontaron sharpshooter that has them in his cross-hairs.
Freema Agyeman (born Frema Agyeman on Mar 20, 1979) is a British actress of Ghanaian and Iranian descent. I suspect that Martha's future with Dr Who will be much like Captain Jack's, she'll pop in and out of Dr Who stories but never stay for long.