She made her acting debut with the film Reckless (1984), and had her breakthrough with the teen comedy film Ferris Bueller's Day Off (1986).
She subsequently earned worldwide fame for starring as Frances "Baby" Houseman in the romantic drama film Dirty Dancing (1987), which earned her a Golden Globe Award nomination.
Her other feature films include Red Dawn (1984), The Cotton Club (1984), Bloodhounds of Broadway (1989), Bounce (2000), Redbelt (2008), The Wind Rises (2013), In Your Eyes (2014), Duck Duck Goose (2018), and Bittersweet Symphony (2019).
Grey's early television work includes the made-for-TV films Murder in Mississippi (1990), Criminal Justice (1990), and If the Shoe Fits as Kelly Carter / Prudence (1990).
She has done voice work in film and television, providing her voice in the 2018 film Duck Duck Goose and the 2008–2014 animated television series Phineas and Ferb.