Peter P. Peters (Fred Astaire), an American ballet dancer billed as "Petrov", dances for a ballet company in Paris owned by the bumbling Jeffrey Baird (Edward Everett Horton). Peters secretly wants to blend classical ballet with modern jazz dancing, and when he sees a photo of famous tap dancer Linda Keene (Ginger Rogers), he falls in love with her. He contrives to meet her, but she is less than impressed. They meet again on an ocean liner traveling back to New York, and Linda warms to Petrov. Unknown to them, a plot is launched as a publicity stunt "proving" that they are actually married. Outraged, Linda becomes engaged to the bumbling Jim Montgomery (William Brisbane), much to the chagrin of both Peters and Arthur Miller (Jerome Cowan), her manager, who secretly launches more fake publicity.
Peters and Keene, unable to squelch the rumor, decide to actually marry and then immediately get divorced. Linda begins to fall in love with her husband, but then discovers him with another woman, Lady Denise Tarrington (Ketti Gallian), and leaves before he can explain. Later, when she comes to his new show to personally serve him divorce papers, she sees him dancing with dozens of women, all wearing masks with her face on them: Peters has decided that if he cannot dance with Linda, he will dance with images of Linda. Seeing that he truly loves her, she happily joins him onstage.