Walton has received 16 Tony Award nominations for his Broadway sets and/or costumes, winning for his work in Pippin, House of Blue Leaves and Guys and Dolls. He has also worked as a director Off-Broadway and in regional theaters, most recently helming a benefit concert of Evening Primrose.

He won an Oscar for All That Jazz and received nominations for Murder on the Orient Express, The Wiz, and Mary Poppins. He won an Emmy for the 1986 television production of Death of a Salesman.