Martial arts aren't strictly Asian. As a matter of fact, martial arts come from nearly every culture that exists.
European Martial Arts:
-Pankration
The goal of this martial art is to bulk up as much as possible, and use as much power as one can muster to hurt the opponent. Fairly simple, yet brutal stuff.
-Savate
French kickboxing, probably influenced from Muay Thai. The style here was also influenced by traditional fencing, only with hands and feet. This is obvious, as the kicks and punches are shot with thrusts rather than swings, and parrying is a skill that can only be gained by a rather hefty amount of experience in the ring, as is feinting. Rather than "belts" for fight ranking, a certain color of gloves are awarded. Golden gloves are the highest. Unfortunately, like fencing, there exist rules of engagement that can hinder a possible victor.
-Boxing
One of the worlds earliest sports. Even in ancient Greece, the sport of boxing would consist of bareknuckle fighting. They eventually added leather straps to the hands, and mounted metal studs or spikes on the knuckles when they wanted fights to end quicker. For a while, it was too brutal and was outlawed by the Romans, but it made a heavy comeback in London. During the 1800's, bareknuckle bouts were often fought and lasted for an ungodly amount of rounds. Eventually, the Queensbury rules were implemented, requiring fighters to wear gloves and take short breaks after some amount of time. Boxing became very popular in the 30's, in America, but eventually made a decline. This is not to say, however, that boxing is not a popular sport here. Boxers are very physically apt, and study a careful science of slipping, bobbing, weaving, feinting, etc. Unfortunately, rules restrict use of low blows and kicking, and clinching happens very often. A boxer could fall victim to an experienced martial artist or wrestler in this fashion. But often, fist fighting is the instinctive way to fight for a human, as is grappling.
-Wrestling
Also a fairly ancient sport, dating back to Greece. Back then, as sport, there were no weight divisions to speak of. There were points for countergrappling and throwing, also, reverses were encouraged. Groundwork is heavily emphasized, and is a very effective sport considering humans most instictively would want to grapple to subdue an opponent rather than pound his head in. Physical fitness is a must. Striking isn't emphasized in this sport, but strikers can be taken down if close enough.
-Vale Tudo
"Vale Tudo" - Portugese for "anything goes." This isn't a style of combat, really, but more of a concept. There aren't really techniques, but rather, it involves getting two fighters in a ring with minimal protection, and seeing how they fare against one another in a street oriented battle. A very good thing here, for learning actual self defense (and offense). In Vale Tudo matches, there are many cases of grappling and groundwork.
And I'm sure that there are arts I haven't listed.
But, all fighting styles, Western or Eastern, have one thing in common; you're moving the human body in some way, in order to overcome another human.
Surely, there are fighters in Illarion intelligent enough to take into consideration the science of unarmed combat.
