Martial Arts have a long history with humanity, and many consider them a fundamental aspect like many other skills and arts. Additionally, with many early space habitats and colonies having heavy restrictions on personal weapons - the need for self-defense once again arose. This has persisted as some restrictions persist even if the safety concerns are just cultural paranoia, and as some habitats focus more strongly on security for the state than the individual. Martial Arts is also deeply cultural, and as such is attached to many communities and groups. The Chinese diaspora and strong cultural connection to "wushu" as an art and in art means that it's hard to find a Chinese-speaking neighborhood anywhere which does not teach one style of the traditional Chinese martial arts, such as Kung Fu. In the LLA, where fitness is as important a cultural aspect as traditional heritage of Earth, many popular styles have remained for fitness purposes, such as Muay Thai, Karate, Jeet Kune Do and Tai Chi. The indian influence on Luna has also kept Kalaripayattu alive. On Mars, the strong media engine and cultural diversity has kept alive many more martial arts for sport, self-defense and entertainment; including Krav Maga, Silat, Taekwondo, Capoeira, etc.
Mixed martial arts and new "synthetic" martial arts also emerge and gain popularity. The difference in environmental conditions, in morphologies, in simple capabilities of the transhuman body, have led to a wide variety of developments in the areas of martial arts. Skillsoft and Teaching software increase the ease of the spread of many styles, as well as teaching XP being a great method for low-level learning of techniques and forms. Gangs routinely drill in basic armed and unarmed arts. Combat sports are made prevalent by the ease of healing and resleeving, leading to events like chess boxing on Titan, cage match fights in many underground rings and the popular "Ultimate Fighter" series by Experia. Almost all security and military personnel drill in hand-to-hand exercises, and for mobile operative who resleeve frequently and may leave their equipment behind, having unarmed or simple weapon combat skills can be invaluable. Below are some examples of modern martial arts in AF 10
"Alpha Arts" is the name for an unofficial collection of fighting techniques used and popularized by many Exhumans, such as Predator clades. It is a synthetic martial art which draws on classic techniques from multiple sources, but combines them with unorthodox use of natural weapons, such as claws, tails and even biting jaws - and also has techniques which allow for more exotic morphs such as utilizing extra limbs or extra senses. It can work in any sort of gravity situation, and is generally designed as an overwhelming and intimidating style which takes advantage of basic transhuman fears and weaknesses to take out an enemy with an unexpected trick - making it advantageous against many classic martial arts. Naturally this reputation means that it is a popular style with rebellious, "edgy" youth across the Solar System.
This is a style of folk wrestling, popularized in certain Scum Swarms or other Scum-like cultures. It is fought bare-handed, usually naked (unless the environment doesn't allow) and utilizes grapples and holds which can be used with or without gravity and by basically any morph which has opposable thumbs. As many swarms have little or no gravity available, the style focuses on short strikes, throws and counter throws to break holds and gain distance and submission holds for the finish. As a sport the style has many variants of rules to constitute a win, but for defensive purposes it should also be noted that many of Bearcat Wrestling's techniques are designed to work even if the user is slowed down by wearing something like a vacsuit.
CANNE DE MATINEE
While not as paranoid as classic orbital or other Near-Earth habs, Venus also still has some concern over the use of penetrating ranged weapons as a self-defense choice. This means melee weapons are among one of the more popular options for a person who seeks to defend themselves, and the effort to create more uniquely Venusian culture and influence from several european cultures led to the creation of Canne de Matinee ("Cane of the morningstar"). This style is an armed style, focusing on blunt weapons of multiple sizes, from batons, to canes to staves. While it can be a sport, it is primarily defensive, focusing on parries, disarms and incapacitating strikes. In addition to classical weapons, Canne de Matinee also teaches techniques to utilize weapons which collapse or which have stun elements.
CHANG'E KUNG FU
The Chang'e school has two competing origin stories. Some say it was developed by particularly cunning Lunar triad and tong members, to get around weapon laws and develop an "honorable" way, while others claim it was developed by anarchist-sympathizers among Chinese vacworkers to fight back against oppressive overseers. No matter the origin, the Chang'e style (named after the Moon goddess) is very popular in the Inner System. It borrows techniques from several other Kung Fu styles and applies them to be used in low or zero gravity situations, including several "mid-air" techniques done while free-floating. Chang'e is also notable because several of it's forms and techniques account for or rely on the prehensile feet of a Bouncer morph.
Sun-Fencing is a post-Fall art and sport, mostly practiced by the Nouveau Riche of Mars. It started as an improvised style using welding or cutting tools by early Barsoomians and evolved into a sport which uses thermic rods modified to be balanced like swords - which leads to limited time "rounds" and a blows with are incredibly damaging even with safety gear making it a very "rocket tag" sport. In addition to the formal setting, Sun-Fencing techniques can still be used with improvised tools, and more commonly with the exotic Plasma Sword (p. 179 Firewall). The style focuses mainly on parries and dodges, with attacks utilizing minimal energy and exposure to make strikes on vital areas which are greatly amplified by weapon choice.
Primal is the premier martial art for hominid uplifts, though other groups study the techniques. It was developed by a couple of Neo-Gorilla Mercurials who synthesized elements from multiple human martial arts to take advantage of the strengths and structure of the uplift form. It focuses mostly on grapples and strikes, utilizing powerful upper body strength to overwhelm and rapidly incapacitate an enemy. Intimidation and dominance displays also are a key feature of Primal and "matches" using the art. Due to the pervasiveness of discrimination against uplifts in some habitats, Primal and it's variants for each Neo-Hominid subspecies are very widely distributed as a self-defense art.
This is a relatively recent art, developed in the past few years when Neo-Avians realized they were one of a few groups without a dedicated style. It was named because they decided Corvids had the most intimidating name. The style emphasizes use of the talons on the feet and the natural weapon of the beak, while the wings and wing-hands are used to block, distract or are left free to evade. The style also teaches techniques adapted from many predatory birds for swooping and diving in flight to attack. Raven School is generally considered very dangerous and even under-handed, it focuses in vital area strikes to cause serious injury and incapacitation and then use the mobility of the avian form to escape or evade.
Steel Fist is a mixed martial art which combines several technique styles to yield maximum efficiency in a synthmorph body. It was developed by synthmorph activists like the Steel Liberators as a self-defense technique and a way to combat oppressive groups even without weapons. Steel Fist drives power in hard strikes and focuses less on grapples or even defense - instead utilizing the hardiness of the synthetic form to prevail against most opponents. Steel fist is very harmful, the innate damaged added by using hard metal or plastic to strike means simple jabs and elbows can deal as much damage as a baton or bat would. Some use it to emphasize the "softness" of biomorphs, but to others it is a technique focused on protecting oneself from a more numerous oppressor. Other similar techniques might be called "Rock-Sock", "Metal Element Kung Fu" or "Lauh-Vinaashak".
Systema Aqua is another mixed martial art which originated on Europa - as several colonial communities there had cultures of martial arts. It borrows from several styles and philosophies and adapts them to be used underwater. While similar to microgravity, water's higher resistance slows techniques and requires them to use more force - Systema Aqua adapts moves which can cut through the water with less resistance, and emphasizes strength and resistance training. The style also can use holds or locks to disable an opponent or target breathing equipment. The style can be used barehanded or with a small knife or one-handed spear. While not widely popular it has found certain niches in aquatic habs among transhumans or humanoid morphs who feel they may be at a disadvantage compared to others. Similar styles exist, such as "Aquanaut Boxing" or "Water Dragon Style Kung Fu".
Tako-jutsu (lit. "Octopus Technique") is a martial art designed by Japanese uplift scientists as a way for Neo-Octopi to train and adjust to using their tentacles for complex dexterity and other uses. It combines the theory and style of schools like Jujitsu or Judo with the flexibility of tentacular limbs and multiple appendages, focusing on throws, holds and counters. While Neo-Octopi are often solitary, the school has remained around both among new uplifts and old as a practical tool of exercise, self-discipline and defense. Rumors abound but are unconfirmed that the Hidden Concern has spent time expanding on Tako-Jutsu to include not just basic exercises and defensive skills, but lethal killing and assassination techniques as well.
Aka "Way of the Desert" in Arabic. This style was developed among Martian Nomads during the early Martial Arts boom on Mars. While North Africa and the Middle East do not have very many unarmed techniques, some nomadic clans were able to borrow elements from French Savate and Turkish Sayokan to build a practical self-defense style. This style is pragmatic, using hands or feet and can be combined with knife techniques. It focuses heavily on using terrain and conditions to your advantage - actively practicing strategy for rough or uneven terrain and approaches for confined spaces (such as inside a tin can or rover) or while riding in a vehicle. It focuses more keenly on tactical thinking and application of theory than rote forms - and is moderately popular as a wholly "Martian" style.
"The Path" is the simple name for the style of unarmed combat developed and taught by the Ultimates. This mixed martial art borrows "the best" techniques and philosophy from thousands of years of combat, allowing one to pick the "appropriate" response to any other style of fighting. The other key thing about The Path is that many of its forms and techniques have been adjusted so they can only be fully performed by a morph with natural capabilities beyond that of a normal human. The speed and strength with which they are executed pushes the limits of the transhuman body. Because of this, outside of the Ultimates the only people who can generally afford to learn The Path are the wealthy or otherwise resource-rich, who can individually or communally afford the advanced morphs which can make use of this style.
Titanian Kickboxing is a sporting and self-defense mixed-martial art drawn from their chess boxing sport. Even if one doesn't chessbox (or its many variants), kickboxing gyms are popular as exercise or self-defense, especially in New Quebec. It draws a bit from traditional sports boxing or kickboxing, and martial art sports like Savate and Sanshou. It uses both punches and kicks, and occasionally throws, sweeps or elbow and knee strikes in self-defense variants. Due to the culture and practical nature of Titan, many defensive techniques involve deflection or evasion in order to stall (as rounds are timed - and security or helpful citizens can't be far off) and many attacking techniques involve painful incapacitation strikes - as for self-defense this is an ideal approach, and such attacks can cause distracting injuries in a match.
ZERO-GRAVITY COMBATIVE TECHNIQUES
"ZGCT" was developed several decades ago by the US Military as a technique for real-world hand-to-hand combat in microgravity. It uses hands or knives, and draws from multiple styles to build a technique and strategy where one can utilize any unanchored limb to attack and can often use inertia and counter-force to their advantage to disable an opponent or gain distance. It also incorporates several bracing and recovery techniques which are useful in a micrograv fight. This is an aggressive, combat style, and typically not for self-defense or sport. All modern militaries either adopted the technique or developed their own similar style - and after the Fall almost every professional military or security operator who might encounter microgravity is familiar with the basics of the style.
Besides just as a "fluff" or "color" element, there are a couple of ways to apply these Martial Arts or any others to the mechanics of Eclipse Phase. The simplest is to treat an individual style as a Specialization for Unarmed Combat (or another appropriate combat skill in the case of an armed art), which applies it's +10 bonus to situations where the style would apply (Such as using a morph with Tentacles for Tako-jutsu, or fighting in low gravity as a Bouncer for Chang'e Kung Fu). This is a very quick, but slightly limiting system, as the bonus is fixed and a character can only ever learn/benefit from a single style (unless spread over multiple combat skills).
An alternative is to treat the Martial Art in question as a knowledge skill. Preferably an Interest, but an Academics or Art could even feasibly be applied. In addition to allowing a character a good outlet to know about techniques, history and practitioners of an art the Knowledge skill can be used to complement appropriate Combat skill checks or even other checks such as Fray when their knowledge of that style applies. This is ideal for characters who have styles which involve multiple forms of attacking (such as a style which is applicable both to empty-hand and knives), and characters who want to learn multiple styles. It also allows much more granularity in skill level with the style; an Ultimate master of The Path might have it rated at a level of 80, while a college athlete only just taking up Martian Sun-Fencing might rate it at 20-30 points.