Liz Shaw first appears in Spearhead from Space, having been drafted from the University of Cambridge by Brigadier Lethbridge-Stewart as a scientific advisor to UNIT. Sceptical at first of UNIT's ambit to defend against alien invasion, she changes her mind when she encounters the newly-regenerated Doctor and becomes involved in defeating the plans of the Nestene Consciousness and its animated plastic Autons.
Doctor Elizabeth Shaw is an accomplished scientist, an expert on meteorites with degrees in several disciplines, including physics and medicine. Her extensive training, however, is still pale in comparison to the Doctor's own knowledge of the universe and scientific principles far beyond those of Earth.
Shaw continues to work with the Doctor and UNIT through encounters with the Silurians, the so-called Ambassadors of Death and the Inferno project. She eventually resigns from UNIT and returns to Cambridge; there was no "farewell scene" on screen for Liz, with her departure simply being announced by the Brigadier at the beginning of Terror of the Autons. She reportedly told the Brigadier that all the Doctor really needed was someone to pass him his test tubes and tell him how brilliant he was; this feeling probably contributed to her decision to return to her own research.
Uniquely of all the companions, she never travels in the TARDIS during her time with the Doctor, her secondment to UNIT coincides with the beginning of his exile to Earth imposed by the Time Lords and the removal of his knowledge of time travel.
Shaw's life after leaving UNIT is not explored in the series. Caroline John appeared as an illusory image of Liz in the 20th Anniversary television movie The Five Doctors, and as Liz herself in the 1993 charity special Dimensions in Time.
In the episode Battlefield, the Seventh Doctor gives Ace a UNIT ID to which Ace remarks that she does not even look like the ID photo, and asks "Who is Elizabeth Shaw?"