Beginning in the late 1920s, pianist, composer, and arranger Mary Lou Williams dazzled audiences in shows and recordings. She wrote and arranged for big-band leaders including Duke Ellington and Benny Goodman, and she was an influential friend and teacher to bebop greats Thelonious Monk and Dizzy Gillespie. But Williams’s wider notoriety was continually undercut by issues with her gender, race, and fierce individualism. Following her from child prodigy to “Boogie-Woogie Queen” to groundbreaking composer and educator, the documentary Mary Lou Williams: The Lady Who Swings the Band sheds light on the traumas and triumphs of this complex and under-recognized artist.