Wu Xia is a film genre from Taiwan and Hong Kong. The name (武俠) is in Mandarin where Wu means martial arts; Xia means heroes. This genre is considered different from Martial arts films. It has its own characteristics.
This genre has been around in the Pacific Rim region since the 1950s or 1960s. The Shaws brothers studio was the forerunner of this type of movies. It was introduced to mainstream Hollywood for the first time in 2000 by Ang Lee's movie Crouching Tiger, Hidden Dragon.
This genre is characterized by its fantasy component. The heroes in the movie practice martial arts to reach a state where they attain any number of superhuman powers collectively known as shen gong, so that they can float in air; scale a cliff or wall; have lightning fast movement; release mystical inner energy (qi) in a form of a beam; paralyze or kill their opponents by hitting their acupressure points with a finger etc. This type of movies usually has a setting in the past so that the audience can justify the fantasy component more readily with an assumption that the methods to practice these supernatural abilities had been lost. There are some occasional Wu Xia movies using the modern settings, but they are usually viewed as unrealistic. When the Star Wars movie came out in the late 70s, many Chinese audience viewed it as a western Wu Xia movie set in a futuristic and foreign world. It is unknown if George Lucas's concept of the Jedi was influenced by the Wu Xia genre. The audience can readily accept the superpower of the mutants as in X-men or an alien as in Superman. However, the same audience may have trouble accepting this type of fantasy because the heroes are supposed to be regular people that possess superpower.
The storylines of this genre are mostly about revenge on killings in the context of a lawless state of society known as Jiang Hu. Crouching Tiger, Hidden Dragon was a rare Wu Xia movie that broke out of this mold.