The story is a Tango. The film alternates between a story about a woman and her choices (then and now) between two men, and with vignettes that show the history of Argentine Tango and how the dance relates to Argentina and its history. The film is dark, but Tango is dark so it fits.
There is a very funny section where they show Tango as seen through the eyes of Hollywood. It includes Abott and Costello dancing Tango and Tango from the Flintstones cartoon.
The dance scenes are all very different. There is a ballet, there is a street dance (much like many of today's music video numbers), there is a stage show (Tango Fantasia), and there is a milonga. The milonga will surprise you, you will want to review this scene over and over.
No Tango afficianado's film collection would be complete if it didn't contain a copy of Tango Bar.