Brest was born in the Bronx, New York, and graduated from Stuyvesant High School in 1969, from New York University's School of the Arts in 1973 and from the AFI Conservatory with an M.F.A. degree in 1977.
His major studio debut was Going in Style (1979), which starred George Burns, Art Carney, and Lee Strasberg, the first of several films to mix action and comedy to great effect. Brest was then hired to direct WarGames (1983), which starred Matthew Broderick, but he was fired during production and replaced with John Badham.
Brest got his big break with Beverly Hills Cop (1984), starring Eddie Murphy. The film grossed over $300 million worldwide and received a Golden Globe Award nomination for Best Motion Picture – Comedy or Musical, as well as an Academy Award nomination for Best Original Screenplay.
Brest's next film was the action-comedy Midnight Run (1988), starring Robert De Niro and Charles Grodin; it was another critical and commercial success. The film, and De Niro's performance, earned Golden Globe nominations.
His work on Scent of a Woman (1992) earned him a Golden Globe Award for Best Motion Picture – Drama. The film also won Golden Globes for Al Pacino and screenwriter Bo Goldman. In addition, the film got four Academy Award nominations: Best Picture, Best Director, Best Screenplay (Adapted), and Best Actor, with Al Pacino winning the last prize.
Brest's next film, Meet Joe Black (1998), starring Brad Pitt and Anthony Hopkins, was a remake of 1934's Death Takes a Holiday. The film received mixed reviews and had a disappointing American box office return of $44,619,100, though it fared much better overseas, taking in an additional $98,321,000 for a worldwide total of $142,940,100.
Most recently, Brest wrote and directed Gigli (2003), starring Ben Affleck and Jennifer Lopez. During filming, production company Revolution Studios took creative control from him, resulting in a radically revised and re-shot version of the original film being released. It became one of the most notorious films of its time, with a scathing critical reception (several critics called it one of the worst movies of all time) and disastrous box office performance. He has not directed another film since Gigli.
In 2009, his New York University student film, Hot Dogs for Gauguin, was one of 25 films chosen by the National Film Registry of the Library of Congress to "be preserved as cultural, artistic and/or historical treasures".