The Cuban Overture was originally entitled Rumba, and was written following a holiday Gershwin took in Havana, on Cuba, early in 1932. It was first performed in New York in August 1932, as part of an all Gershwin programme, which also included the Piano Concerto in F and An American in Paris. He changed the title later the same year to reflect the work's considerable complexity.

The overture is rich and intricate, from the bitter-sweet motif at the start, soon followed by three tunes developed in counterpoint (i.e. simultaneously), through the beautiful middle section, to the exciting return of the rumba rhythm at the end. But it is dominated by the Caribbean rhythms and Latin American percussion section that earn it its title, and its popularity.