The Martial Arts are a collection of combat oriented, or once combat focused systems that can be found virtually everywhere in the world--not just in Asia. Unlike brawling, the martial arts are systemized, grounded firmly in principles, and contain a higher knowledge. Contrary to popular belief, the practice of martial arts has nothing to do with religion. Although some do practice it as a lifestyle--and that is purely up to the practicioner--it is perfectly fine for a Christian to practice martial arts.
So what about the violence? Well the movements are like any other exercises for the most part, just combat oriented. However, the object of martial arts is to avoid and end violence, not provoke, encourage, or keep it going. Not all martial artists practice martial arts for self defense.
Some of the benefits of correct martial arts training:
Sharpening of mind
Focus
Calmness mind under stress
The ability to defend yourself if need be
Physical Fitness
Confidense, but also humility
Self-Discipline
Improved reflexes, coordination, balance, speed and strength