A pair of rival schools of martial arts, run by a pair of masters who have probably been feuding for years before the series even started. If dojo is applied to non-Japanese martial arts, its use is an example of the Far East trope.
Most often, but not always, the two masters were students of the same martial arts style before branching off to different styles: the protagonist usually (but not always) learning under the benevolent master who teaches wisdom and self defense, while the rival school is run by an Evil Mentor who encourages its students to be ruthless, aggressive and brutal. A tough Sensei for Scoundrels who takes the pragmatic middle-of-the-road approach could substitute for either of them.
A subset of this trope comes in the form of members of one school (or even an unaffiliated challenger looking to show his prowess) going to the other dojo and challenging the sensei or top student to a match, usually as an excuse to then completely ransack the dojo, maim everyone inside, and steal a memento of their victory (typically the dojo's marquee). This kind of act, whose exact term is dojoyaburi (道場破り, "dojo storming"), is Truth in Television, and there are stories about brutal dojo wars in historic Japan and more recently in the Brazilian vale tudo scene.
Very often comes up in Fighting Series. This situation often involves or ends with the main students from both schools eventually becoming friends or at least allies (usually after one of them defeats the other), effectively ending the feud, or turning it into a friendly rivalry (if it wasn't already) instead.
- Being the quintessential Fighting Series (at least in Manga), Dragon Ball of course has this, with Goku learning the Turtle Style from the Muten Roshi, while his rival Crane Hermit's teaches his students styles of brutal assassination. Goku fights two members of the Crane School, the Crane Hermit's brother Tao Pai Pai and his star pupil, Tenshinhan. Tenshinhan defeats Goku the first time, but, in a rare occurrence for this trope, his HeelFace Turn begins even before Goku eventually bests him.
- The two styles get revived after the events of Dragon Ball Z in Dragon Ball Online, though the rivalry is more friendly in nature since they're headed by Kuririn/Krillin and Tenshinhan. There's still a schism between their philosophies, inspired by what each took away from their time fighting alongside Goku: the New Turtle School is all about playing support, while the New Crane School focuses on performing powerful, decisive ki attacks.
- Pokémon did an episode about a pair of rival Gyms. Each of them tried to be official Gyms, but in the end, neither of them were worthy enough to be declared as an official Gym.
- The games also featured this with Saffron City's two Gyms, one for the Fighting-type and one for the Psychic-type. Only one got to be the official Gym of the city, and the Psychic-type Gym won due to Elemental RockPaperScissors.
- Bamboo Blade has rival Kendo schools.
- Kenichi: The Mightiest Disciple has the Ryozanpaku Dojo vs. the criminal organization YAMI. They both are run by superhuman martial artists (that have Charles Atlas Superpower to the point they are "Physical God"-level badasses), and they re both (in a way) Arrogant Kung-Fu Guy-types (only the former is the "Condescending Compassion because they are the only ones that can fight other Masters" type vs. actual murderous arrogance), and their conflict essentially boils down to "Thou Shalt Not Kill and use martial arts to protect people vs. martial arts should be used to kill people and lord over them".
- On the dojoyaburi subset, Ryozanpaku gets challenged once in a while... And has a number of specific rules designed to extort the challengers, and once they win they force them to get cured at the clinics of two of their members for an outrageous fee. In Ryozanpaku's defense, they're very poor and extorting challengers is one of their main ways to fund themselves... And the cures they provide are actually worth more than the challengers are forced to pay (Kenzei and especially Akisame are that good).
- Jackie Chan's first starring role, Snake in the Eagle's Shadow, is about two rival schools, Snake Hand and Eagle Claw. Eagle Claw has exterminated almost every student from Snake Hand. Jackie becomes the last student of the Snake Hand, and incidentally is able to fight the master of Eagle Claw without being killed, so he learns about his style and combines both of them into the style that names the film.
- The central conflict in the Bruce Lee film Fist of Fury is between the hero's Chinese kung-fu school, and an antagonistic Japanese karate school. By the end, an open conflict between the two schools has left everyone dead except for a few of the hero's friends from the kung-fu school.
- Star Wars: The original trilogy establishes the Light and Dark sides of the force, mastered by Yoda and Darth Sidious, respectively. The Jedi and the Sith teach opposing philosophical approaches to similar martial and magical skill, and have been at each others' throats for twenty-five thousand years.
- Supported by Miyagi Dojo vs Cobra Kai in The Karate Kid (1984) and The Karate Kid Part III. The rivalry gets revived years later in Cobra Kai, when Johnny Lawrence revives the titular dojo and Daniel in-turn revives the Miyagi-do. Sadly, Reality Ensues, and by the end of season 2 the heady mixture of resentment, petty feuds, vandalism and one-upmanship explodes into an outright war, leaving multiple students from both dojos injured, permanently disabled and in one case possibly dead.
- Ninja Academy. Oddly enough, one of the students at the Hero ninja academy is a mime.
- Fist of Legend has the local kung fu school as rivals of the karate dojo of the occupying Japanese. The Chinese are the heroes and the Japanese are the villains, though the most powerful Japanese master is unaffiliated with the local dojo and stands neutral in the feud.
- The Gone-Away World by Nick Harkaway has a rivalry between a ninja school and a mime school. (Yes, the mimes are martial artists. Don't ask.)
- As they draw significant influence from European Swordsmanship, (see Real Life below) the Elsabeth Soesten books have this come up quite often. In Bait And Switch Elsabeth and Husson nearly get into a duel over the superiority of their respective masters.
- Bobby Wasabi's (whose local sensei is an Adult Child Big Brother Mentor) and the Black Dragons (a Cobra Kai Expy) in Kickin' It.
- In Ninpuu Sentai Hurricaneger and Power Rangers Ninja Storm, three Rangers are from the Hayate/Wind Ninja Academy and two are from the Ikazuchi/Thunder Academy. They clashed at first with the Thunder ninjas acting as Psycho Rangers to the Wind trio, but eventually pulled together to fight the Big Bad.
- Almost the entirety of Juken Sentai Gekiranger is about the battles between the heroic GekiJuken Beast Arts school and the evil RinJuken Akugata school. They wind up joining forces to defeat the Long and his GenJuken school after Rio discovers he and the rest of the RinJuken Akugata have been manipulated by Long.
- This was the whole point of the FWA Academy vs. WAW Academy - Academy Warfare event. This was mostly put on, since the academy happened to share some of their students, mostly.
- Coastal Championship Wrestling saw a rivalry between CCW's Bodyslam University and Main Event Training Center after Pablo Marquez left Bodyslam and founded Main Event in protest to Bodyslam's head trainer, Cash Money Alex G, abuse of female students. As it is also in Ft. Lauderdale Florida, The Spot can sometimes act as a third wheel. For those of you worried, this rivalry was just an angle to give CCW Wrestlers something to fight over, Alex G doesn't actually try to hurt students, female or otherwise.
- Jade Empire naturally has a variant on this (It's technically the same school, but the two teachers use different styles). You get to decide which master's teachings come out on top.
- Pokémon Red and Blue: The current official Gym in Saffron City is dedicated to the Psychic-type under Sabrina. Immediately next door is the Fighting-type dojo, which used to be the sanctioned Gym until Sabrina and her followers crushed it, though they still devote themselves to the practice. And then the Player comes along and sacks the Fighting-dojo a second time, forcing the Karate King to beg him not to take their emblem, instead offering up one of their prize Pokemon.
- Judo founder Jigoro Kano had to defeat several other jujutsu schools, among them Teshin Yoshin-Ryu and Ryoi Shinto-Ryu, in order to push his own and create the art as we know it. Ironically, he had to endure a massive loss when his school lost to the Fusen-Ryu faction, from where he brought the groundfighting principles to his art.
- So common was this in Japan that Kyokushin karate founder Mas Oyama kept baseball bats on his dojo in case of a dojoyaburi.
- In Brazil, the Brazilian Jiu-Jitsu and luta livre schools were bitter enemies, as they featured opposite combat philosophies and taught different social demographies (BJJ was the martial art of the high class and Brazilian elite, while LL dojos were cheaper and friendlier to lower classes and poor people). Eventually Brazilian jiu-jitsu side, led by the ubiquitous Gracie family, got the upper hand and expanded internationally via the Ultimate Fighting Championship, while luta livre became a shadow of itself and almost faded out.
- Within the Gracie clan of Brazilian jiu-jitsu schools, Hélio and Carlson Gracie's schools were rivals due to their different approaches to grappling, while another branch of BJJ led by Oswaldo Fadda was against the Gracie doctrine overall.
- New Japan Pro-Wrestling, which boasted that professional wrestling was the strongest martial art in the world, was notorious for shutting the doors to its dojo when someone came in to challenge any of the professional wrestlers and then giving out No Holds Barred Beatdowns to the unlucky challengers.
- Count Dante's Dojo Wars.
- Comes up throughout the history of European Swordsmanship as well. The rivalry between the Brotherhood of St. Mark and Federfechter in particular stands out, as the former held a monopoly on instruction in the Holy Roman Empire, which the latter infringed upon.