Young's early roles include the independent romance Jane Austen in Manhattan (1980) and the comedy feature Stripes (1981), the latter being a commercial success.

She then played the female lead, Rachael, alongside Harrison Ford in the classic science fiction film Blade Runner (1982).

On television, Young played the female lead opposite Lenny Von Dohlen in Under the Biltmore Clock (1986), based on F. Scott Fitzgerald's story Myra Meets His Family.

[6] One of Young's most prominent roles was as the lover of a ruthless Washington politician (Gene Hackman) in No Way Out (also 1987), alongside Kevin Costner.

Her other credits include Dune (1984) (playing Paul Atreides's love interest Chani), Baby: Secret of the Lost Legend (1985), and Fatal Instinct (1993).

She was next cast as Vicki Vale in Tim Burton's film Batman (1989), but during rehearsals, she broke her arm after falling off a horse and was replaced by Kim Basinger.

In an unsuccessful attempt to win the role of Catwoman (which was originally offered to Annette Bening but, after Bening became pregnant, Michelle Pfeiffer was cast) in the sequel Batman Returns (1992), Young constructed a homemade Catwoman costume and attempted to contact Burton and actor Michael Keaton during production.

[6] She appeared on The Joan Rivers Show in character as the Catwoman, campaigning for the role and making a plea to Tim Burton.

Young has appeared in independent films, including roles in Poor White Trash (2000), Mockingbird Don't Sing (2001), and Sugar & Spice (also 2001).

In 2008, Young competed in the television program Gone Country 2, which included a competition in a celebrity demolition derby at the Henry County Fairgrounds in Paris, Tennessee.

[13] During the interview, she described how she was now looking for movie work after raising her two sons, and produced a short video clip promoting her job search which Letterman played.

[14] Young reprised her 1982 role of Rachael for Blade Runner 2049 (2017), portraying both the original (using archival footage from the first film) and a brand new cloned version of the character.

[24] In August 2018, Young and her son were identified on surveillance video removing two MacBook laptops from the Astoria, Queens production office for the film Charlie Boy.

[25][26] Young released a statement the day after initial reports were posted, saying that she "gathered what I believed to be my property but later discovered I was mistaken" and had contacted members of the office to return the items.