This Guardian reviewer declares it his favorite film and says, "There are many reasons to adore the film, most obviously its almost unworldly, dream-like beauty." DVD Talk calls it "a phenomenal picture; a marvelously acted tale of longing that is moving and often stunning in appearance. It's definitely a must-see."
Senses of Cinema has a lengthy article that says,
Wong’s key elements –what older critics might call “atmosphere” and “characterizations”– are thus grounded in abstraction rather than plot, and it’s hard to think of a recent movie that offers just such abstract ingredients that are by themselves sufficient reasons to see the picture. But it is precisely this quality of aesthetic abstraction that makes up an ideal dreamtime of Hong Kong, which is Wong’s ode to the territory.Roger Ebert calls it "a lush story of unrequited love that looks the way its songs sound." Rotten Tomatoes has a critics score of 90%.
There's a segment of an online film criticism course devoted to this film:
from this video: "It was released in 2000 and hailed an instant classic, winning awards all over the globe". I'm glad I'd seen the movie before I watched this; but this offers a helpful exploration of the movie, including technical elements and the social and political context.