Young began her film career in 1980 in the film Jane Austen in Manhattan, followed by a small role in the 1981 film Stripes, and played female lead in the part of a replicant opposite Harrison Ford in the futuristic classic Blade Runner (1982). She had a small role in the film Wall Street as the wife of Michael Douglas' character. Her role was originally intended to be larger, but was significantly reduced due to clashes with Oliver Stone.
One of her most prominent roles was as the mistress of a ruthless Washington politician in 1987's No Way Out, playing opposite Kevin Costner. Other notable credits include Dune, Fatal Instinct, Ace Ventura: Pet Detective and Baby: Secret of the Lost Legend.
In 1988, Young appeared in The Boost with James Woods.
She was cast as Vicki Vale in Tim Burton's 1989 successful film Batman. During rehearsals, however, she broke her arm after falling off a horse and was replaced by Kim Basinger.