There is no cinematic iconography more emblematic of the Hollywood musical than the dancing figures of Fred Astaire and Ginger Rogers. In Stevens's film, dance is used as an expression of romantic developments, a device typical of musicals of the 1930s. In the film, Lucky Garnett (Fred Astaire), a dancer and sometime gambler, arrives late for his marriage to Margaret Watson (Betty Furness) only to find that her furious father, the judge (Landers Stevens), has called off the wedding. The judge challenges Lucky to go to New York and earn $25,000 in order to win back Margaret's hand. In New York, Lucky meets Penny (Ginger Rogers), a dance instructor, who loses her job as a result of their chance encounter. The pair are, however, sent to audition at the Silver Sandal nightclub, where they eventually dazzle the patrons and are hired. When Margaret arrives in New York to tell Lucky she has met and fallen in love with another man, Lucky and Penny are free to pursue their relationship as lovers and dancers.

Swing Time marks the introduction of special effects into Astaire's dance routines. In the "Bojangles"number, Astaire dances with huge shadows of himself. To achieve this effect, the dance was filmed twice under different lighting conditions. The version with the strong shadow was then optically tripled in the lab and combined with the film made under standard lighting.