Martínez was signed by the Los Angeles Dodgers as an amateur free agent on September 1, 1984 and was the youngest player in the National League when he made his major league debut on August 13, 1988 against the San Francisco Giants.
He had a breakout season in 1990, when he won 20 games, struck out 18 batters in a game (on June 4), was selected an All-Star, and finished second in strikeouts as well as in the Cy Young Award balloting.