Elizabeth "Liz" Shaw was a civilian member of UNIT. She did much field work and upon one occasion became acquainted with the Third Doctor.
From then on, Liz helped Doctor while at UNIT. This often involved her winding up in the same life-threatening situations as the Doctor. She continued to work occasionally at UNIT even after leaving their regular employment. She was an accomplished scientist and an expert on meteorites. She had degrees in several disciplines, including physics and medicine.
Liz was drafted from the University of Cambridge by Brigadier Lethbridge-Stewart as a scientific advisor to UNIT. (Lethbridge-Stewart did not know at that time that the Doctor had arrived on Earth and would ably serve as UNIT's scientific advisor.) Skeptical at first of UNIT's remit to defend the Earth against alien invasions, she changed her mind when she encountered the newly-regenerated Doctor and became involved in defeating the plans of the Nestene Consciousness and its animated plastic servants, the Autons.
Liz's extensive training paled in comparison to the Doctor's own knowledge of the universe and scientific principles far beyond that of Earth's. Eventually, she resigned from UNIT and returned to Cambridge.
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.
Liz holds the distinction of being the only full time companion to never take a trip in the TARDIS