For her performance in Killing Eve, Shaw won the 2019 BAFTA TV Award for Best Supporting Actress. For her performances in the second seasons of Killing Eve and Fleabag, she received Primetime Emmy Award nominations for Outstanding Supporting Actress in a Drama Series and Outstanding Guest Actress in a Comedy Series respectively. For the third season of Killing Eve, she was again nominated for Outstanding Supporting Actress in a Drama Series.Shaw has worked extensively with the Royal Shakespeare Company and the National Theatre. She won the 1990 Olivier Award for Best Actress for various roles, including Electra, the 1994 Olivier Award for Best Actress for Machinal, and the 1997 Drama Desk Award for Outstanding Solo Performance for The Waste Land. Her other stage work includes playing the title role in Medea in the West End and on Broadway (2001–2002). She was awarded an Honorary CBE in 2001. In 2020, she was listed at No. 29 on The Irish Times list of Ireland’s greatest film actors.