Twilight: Los Angeles, 1992 has won several awards. These include the Outstanding One Person Show award for Anna Deveare Smith at the Drama Desk Awards, the Outstanding Sound Design award for John Gromada at the Drama Desk Awards, and the Outstanding Special Effects award for Batwin & Robin Productions at the Drama Desk Awards. Additionally, Anna Deavere Smith received a Special Citation from the New York Drama Critics Circle Awards, George C. Wolfe won the Best Director - Play award at the Outer Critics Circle Awards, and Anna Deavere Smith received a Performance award from the Theatre World Awards.