While "I know kung fu" is one of Neo's most famous quotes from The Matrix, he uses a variety of martial arts styles across the four Matrix movies. In addition to their mind-bending plots and philosophical concepts, the films became known for their high-flying martial arts action that was uncommon in American movies at the time. Similar to the Hong Kong wuxia movies that inspired the Wachowskis, Neo uses a mixture of Asian traditional martial arts in The Matrix and its sequels.
For The Matrix's fight choreography, Lilly and Lana Wachowski turned to legendary Hong Kong filmmaker Yuen Woo-ping, who has also worked on titles like Drunken Master, Kung-Fu Hustle, and Ang Lee's Crouching Tiger, Hidden Dragon. Yuen incorporate many of the techniques used in wuxia movies into The Matrix, including suspending actors from wires to create fluid and larger-than-life action scenes. As part of the preparation for the movie, Yuen had Matrix lead Keanu Reeves and the rest of the cast undertake four months of martial arts training in a variety of styles.
The fights in The Matrix movies are intended to be cinematic more than realistic, based on the characters' ability to literally control the world around them, but many of the individual strikes and techniques used can be identified as belonging to particular martial arts traditions. After Morpheus's training, The One likely has access to every style of fighting, or at least the ones that had been preserved into the dark future of The Matrix. These are the styles that are most recognizable in the fight scenes from The Matrix and its sequels.
Kung Fu
Keanu Reeves loves kung-fu movies, and the Chinese art of kung fu is the bedrock of his character Neo's fighting style in The Matrix. In China, "kung fu" is something of an umbrella term referring to a multitude of traditional martial arts styles, but it is specifically identified with the kind of animal-inspired stances that Neo and Morpheus strike in their fight with each other inside their virtual dojo, including the easily-identifiable crane stance. The emphasis on punches and kicks, as opposed to grappling and close-distance strikes, is another way in which kung fu is the strongest influence on Neo's fighting style.
Wing Chun
Wing Chun, also known as Chinese boxing, is a hand-to-hand technique which focuses on using quick hand techniques to block opponents' strikes and retaliate. Neo uses Wing Chun during his fight with Laurence Fishburne's Morpheus in The Matrix during the sequence where the two are trapping each other's hands. He later uses similar blocking techniques in his fight with Agent Smith in the subway.
Jujutsu
Jujutsu, also Romanized as jiu-jitsu, is a Japanese martial art that uses holds and throws to immobilize the opponent. Today, jujutsu is perhaps best known through its Brazilian variation, which is commonly used in mixed martial arts competition. Jujutsu is one of the martial arts Neo is shown having loaded into his brain in The Matrix, and it appears later in the film when he is grappling with Agent Smith. Neo makes more use of jujutsu in The Matrix Resurrections, where his fighting style is closer to John Wick.
Aikido
Aikido is another Japanese martial art that aims to use the opponent's momentum against them, and is perhaps best known in cinema as the martial art used by Steven Seagal. Morpheus uses a number of aikido throws during his training session with Neo. Neo goes on to use aikido-style throws in his own fights, such as against the Merovingian's henchmen in The Matrix Reloaded.
Kenpo
Kenpo is one of several martial arts included in the list of tapes loaded into Neo's brain in The Matrix, although the movie uses the Americanized spelling of "Kempo." Literally meaning "method of the fist" in Japanese, the term kenpo is used to refer to multiple styles, but is typically a type of full-body karate that emphasizes fighting multiple opponents in its kata. This proves helpful for Neo when he has to take on multiple opponents, such as the copies of Agent Smith in The Matrix Reloaded.
Drunken Boxing
Drunken boxing, also known as zui quan, is an unorthodox Chinese style which aims to mimic the style of a drunk person to disorient the opponent. This can be seen in Neo's dojo fight with Morpheus, where he adopts a more relaxed stance after their initial exchange. Drunken boxing is another area where The Matrix displays the influence of Yuen Woo-ping, who directed Jackie Chan's breakthrough movie Drunken Master.
Taekwando
Neo also showcases taekwando-style kicks in his subway fight with Smith, including a flurry of kicks to the head. Taekwando is a Korean style that focuses on powerful kicks by developing speed and flexibility. This style is also seen in The Matrix in Trinity's famous flying kick.
Bojutsu
While Neo mostly fights hand-to-hand or with guns, he also uses the Okinawan art of bojutsu, fighting with a staff. In his Matrix Reloaded fight with Agent Smith and his clones, Neo uses a metal pole as an improvised bo staff to help fend off his multiple opponents. The influence of bojutsu can also be seen in the subway fight in the first Matrix, where he pivots off a subway pillar in his fight with Smith in the same way a fighter would use a bo.
Tai Chi
Tai chi is an ancient Chinese martial art that is typically practiced for health reasons as well as self-defense. However, there have also been a number of legends and myths attributing supernatural powers to tai chi masters, including the powers to fly and stop bullets. Neo stopping bullets was one The Matrix's most iconic scenes and was echoed in the sequels. These "bullet time" effects were hugely influential and much-imitated in Hollywood movies of the 2000s. While stopping bullets with chi energy is mythology instead of practical martial arts, the more legendary attributes of tai chi show how even the science fictional elements of The Matrix were heavily influenced by martial arts. Keanu Reeves was obviously personally influenced by the style as well, later directing and starring in the movie Man of Tai Chi.