Liz Warner, as she first appears, is a decorated FBI agent, and one of the major love interests of Special Agent Don Eppes. Don was originally her instructor at Quantico, and while there seems to have been a mutual attraction, that professional relationship precluded a personal one, according to the rules.
Liz crops up a couple of times, starting with "Longshot", before becoming part of the team and a fixture in Don's love life. She declares the romantic relationship to be definitively over in "Chinese Box", but remains a close and trusted personal friend.
She is extremely intelligent, competent, engaging and loyal, but like Don seems to struggle with building more personal, intimate relationships. Liz is planning to stay with team despite David's 'desertion', at least for the foreseeable future.