Peter P. Peters (Fred Astaire) is a professional ballet dancer, but what he really wants to perform is more modern. He likes to practice tap in his quarters, but his manager, Jeffrey Baird (Edward Everett Horton), is horrified at the notion and wishes he would stick to what makes him one of the most famous ballet dancers in the world, known globally as Petrov. So the American Pete has to pretend to be Russian in his professional life, but what is really intriguing him at the moment is another celebrated dancer, Linda Keene (Ginger Rogers) - how can he meet her?
After the masterpiece that was Swing Time, it was natural that it would be hard to follow up with a work of equal quailty, and there was by the time of Shall We Dance (no question mark in that title for some reason) audiences getting the "seen it all before" feeling about Astaire and Rogers' terpsichorean antics. This was a little unfair, as while this effort did seem too protracted and keen to focus on past successes it did have quite a few highlights, and the George and Ira Gershwin songs were not be sneezed at either.
The plot takes the usual misunderstandings that were par for the course in such films by this stage and brings them into more risqué territory, for 1937 at any rate. At first Pete keeps up his Russian act with Linda, who says she has had it with amorous dancers, so she thinks he is some kind of madman, but when they happen to board the same ship to New York she overhears him talking to the press in his natural accent and is not impressed, letting him know it too. Therefore it is up to Pete to spend the rest of the voyage attempting to romance Linda and after a fashion, he's quite sucessful.
At least until the rumour hits the media that they are actually married, thanks to Jeffrey's blundering in trying to persuade one Lady Denise (French actress Ketti Gallian) that Pete won't be interested in her. So it is that not only does gossip say they are married when they were just getting acquainted, but that Linda is pregnant, a twist that was pretty near the knuckle for a frothy musical comedy of its day. Linda flies off the ship in a plane (and in a huff) and Pete is left to pick up the pieces, taking the misunderstandings to fresh heights of convolution.
Not least when the couple have to actually get married so they can divorce to tell the newspapers that it's all over between them so people will truly believe them. It's a mark of the style of the films of this duo that you are happy to go along with this of it means we are rewarded with another dance number or a song of the calibre of "Let's Call the Whole Thing Off" or "They Can't Take That Away From Me", two of the hits from the soundtrack. Needless to say the hoofing is top notch, with even a performance on roller skates, although the final routine is rendered slightly unnerving by the chorus girls holding masks of Ginger's face up to their own. And the insistence on featuring ballet is a shade too stuffy for a musical that should have been unconcerned with the highbrow - rumour had it Fred was unhappy with this approach and if true, he was quite right.