Equus has won several awards, including Best Play at the New York Drama Critics Circle Awards and the Outer Critics Circle Awards. The show also received awards for Outstanding Costume Design (Drama Desk Awards) for John Napier, Outstanding Director - Play (Drama Desk Awards) for John Dexter, Outstanding Lighting Design (Drama Desk Awards) for Andy Phillips, Outstanding New Foreign Play (Drama Desk Awards) for Peter Shaffer, and Outstanding Set Design (Drama Desk Awards) for John Napier. Additionally, the cast received recognition, with Anthony Hopkins and Peter Firth winning Best Performance at the Outer Critics Circle Awards, and Peter Firth also receiving the Best Young Player award at the Outer Critics Circle Awards. Peter Firth was further honored with a Performance award at the Theatre World Awards.