Talking Heads has won several awards, including the Outstanding One-Person Solo Performance at the Drama Desk Awards for Alan Bennett. Alan Bennett also received the Best Foreign Play award at the New York Drama Critics Circle Awards. Valerie Mahaffey, Lynn Redgrave, Kathleen Chalfant, Daniel Davis, Christine Ebersole, and Brenda Wehle all won Performance awards at the Obie Awards. Additionally, Michael Engler won the Outstanding Director of a Play award at the Outer Critics Circle Awards. Talking Heads also received the Outstanding Off-Broadway Play award and Special Awards at the Outer Critics Circle Awards.