Compassion

Compassion was a remembrance of a Human who joined the Remote. She traveled with the Doctor, during which time she evolved into a living TARDIS.

Biography
Compassion was originally Laura Tobin, a woman residing on the original colony of the planet Anathema. She, like all the colony residents, either was or became sterile. They therefore reproduced using Remembrance Tanks, and over the millennia that the ship that Anathema was based upon took to get to Earth, all the colonists were "remembered" using biomass inside the remembrance tanks. Compassion is the result of this process. (EDA: Interference - Book Two)

Compassion was a member of the Remote, an offshoot of Faction Paradox. Following her encounter with the Doctor on Earth she chose to travel with him and Fitz (whom she, as Laura Tobin once knew). She also knew Kode, who was the remembered version of Fitz).

As Compassion came from a media/signal orientated culture she always wore an ear piece (or receiver), the Doctor interfaced her receiver with the TARDIS systems to protect her from any 'harmful' signals she might encounter during their travels. This interface had unforeseen results, warping her biodata along Block Transfer Computations, culminating in her 'birth' as a sentient TARDIS. (EDA: The Shadows of Avalon)

The Time Lords pursued her, the Doctor and Fitz travelling within her and eventually made forced arrival on Gallifrey just before the Faction Paradox attack and Gallifrey's eventual destruction. After the destruction of Gallifrey, she dropped off the Doctor on 19th century Earth, dropped off Fitz Kreiner on 2001 Earth, and left to explore the Universe with a Gallifreyan technician, Nivet. (EDA: The Burning, Escape Velocity).

After an unknown amount of time, she's contacted by the embodiment of human technology, they strike a deal that results in the creation of the City of the Saved (FP: Of the City of the Saved...). The City exists just beyond the end of the current universe and the creation of the next.

Other information
Physically, a fictionalised version of Compassion evidently resembled the actress Nicole Kidman. (EDA: Interference - Book Two). However, she is described (less flatteringly) as being "gerbil-faced and chubby". This description (and interestingly the other) fluctuate throughout the series with Fitz thinking she's rather plain but with enough "curves" to make her appealing.

Behind the scenes
Compassion is one of the only ongoing characters from Doctor Who to also appear in the spin-off book series, Faction Paradox.