Wong Kar-wai, 2000. Neighbours in 1962 Hong Kong realising their spouses are having an affair with each other. Often-cited 21st-century best film.
From Wikipedia
In the Mood for Love is a 2000 romantic drama film written, directed, and produced by Wong Kar-wai. An international co-production between Hong Kong and France, the film follows a man and a woman in 1962 who discover that their spouses are having an affair. As they spend time together, they gradually develop feelings for one another. It is the second installment in an informal trilogy, preceded by Days of Being Wild (1990) and followed by 2046 (2004).