More than just an Asian Fight movie.
A lot of Asian movies involving martial arts fall into the trap of relying far too heavily on the fight scenes and loose focus on other aspects, such as plot, and backdrops. This movie blends all the elements of a good movie including the fight scenes but doesn't rely on them.
Here we have two stars of the Asian movie scene, Chow Yun Fat and Michelle Yeo, plus a relatively newcomer of Zhang Ziyi. All three had major parts in the movie, it could be argued however that Zhang had the more complex character.
She had to combine the nobility of a princess, the inexperience of youth, and role of a fighter. As she plays a princess, she is expected to marry a suitor that has been arranged for her.
As for the plot, we have a warrior (Chow Yun) who wishes to retire giving his sword the Green Destiny to an old friend (Michelle). It seems that the two of them have been more than friends in the past. The sword however is stolen, so now the investigation is on. This leads to the house of Yu where we meet Zhang, from this point the movie adds another element over the "traditional" Asian martial arts movie.
There is a reason it was nominated for so many awards, it is an excellent movie. If you like Asian/martial arts movies, you should watch this one.