Richard has been writing, directing and creating contemporary forms of theatre for five decades. His plays have received productions throughout Australia and internationally, and he has worked as a director in Melbourne, Sydney, Adelaide, Toronto, New York, Amsterdam, Utrecht and Ghent.

His plays include: Quick Death (1979), Slow Love (1983), Dolores and the Department Store (1999), The Inhabited Woman (2003), The Inhabited Man (2009), The Darkening Sky (2019)

Recent Productions include: A double bill of Quick Death and Slow Love (La Mama, 2015); a double bill of two Belgian plays, Four Men and Dog Play (Elvis Peeters: La Mama, 2017); In the Solitude of Cotton Fields (B-M Koltes: La Mama, 2019); Broken River (Tony Reck: La Mama, 2019), and The Darkening Sky (Murphet: Theatre Works, 2021).

Murphet worked at the Victorian College of the Arts for two decades where he was Head of Drama (2007- 2009) and Head of Postgraduate Studies (1996 – 2006). He was a member of the Australian Performing Group, and the Artistic Director of the Mill Theatre Company. He was awarded a Lifetime Achievement Award for his work in theatre at the Australian Greenroom Awards (2017). His book on Late-Modernist theatre practice, Acts of Resistance, was published by Brill Publications, Amsterdam in 2020.