Generally considered one of the two best Fred and Ginger movies (along with my favorite, Top Hat). An Oscar winner for "The Way You Look Tonight", which is perfectly sung by Astaire, but which is a bit spoiled by the fact that Rogers has her head covered in shampoo during the scene. The score, by Dorothy Fields and Jerome Kern, also includes "Pick Yourself Up", "A Fine Romance", and "Never Gonna Dance". The plot is the usual Fred and Ginger trifle ... the plot is never the point of their movies.
The dance highlight is "Never Gonna Dance" (many of these clips are of poor quality, especially unfortunate since Criterion has recently released a restored version):
The most famous dance in the movie is "Bojangles of Harlem", a tour de force as a dance and as a production, that is problematic because Astaire wears blackface. This time, it's hard to get a clip that shows the entire number, so here's an excerpt:
Finally, here is probably the best dance number in the film, "Waltz in Swing Time":
Bonus, because I can never resist posting it again: the greatest scene in Fred and Ginger history, one that never fails to bring tears to my eyes: