I can see why this is considered one of the best films of the 21st century (maybe a bit early to tell since we're less than a quarter through the century, but a list titled "best films of the 21st century" is understandably more dramatic—and click-worthy—than "best films of the first 22 years of the 21st century").
Every shot in the film is a work of art. The colors (and set design and costume design, all related) are incredible, vibrant yet muted and kind of nostalgic. Acting is great. The plot is amazing, on the surface it's the "love story" (quotation marks because it's very untypical, not sure it should even be referred to as one) of two neighbors who (spoilers!) discover that their respective spouses are having an affair together. Underneath, it's about dealing with loss. The theme is sculpted into the film's very environment, with Wong Kar-wai setting it in a lost, romanticized version of 1960s Hong Kong, its lights and stairs and alleyways and cramped apartments.
The only thing I liked a little bit less was the ending, I thought it tried to say a bit too much, to explain things that could have been left unexplained. Also in the last 20 min or so, the film is suddenly not set exclusively in Hong Kong, but also in Angkor Wat (??) and some of it feels like a Visit Cambodia ad. The most important word of the film's title is "mood", not "love", and that mood is kind of lost when we leave Hong Kong.