Bruce Lee is probably the most famous martial artist in history. People all around the world tried to find martial arts schools after seeing him wipe the floor with bad guy after bad guy in his movies. He also contributed a great philosophical and practical work of the martial arts, "The Tao of Jeet Kune Do".
What mister Lee proposed was an answer to what he called "the classical mess".
All the different people of the world have developed their own styles of hand to hand and armed combat, as self defense has always been a necessity. And all of those styles and forms had some deadly effective techniques. The problem as he saw it was their tendency to isolate themselves in their own schools.
In this way his Jeet Kune Do was a philosophical forerunner of what we now call MMA, or Mixed Martial Arts which is both a sport and an ongoing quest for the ultimate fighting style. The underlying philosophy was and remains that one should take those things from every discipline they could that were most effective for them.
So depending on your body type, strengths and weaknesses you might find elements of Brazilian Jiu-Jitsu and Muay Thai which are very complimentary styles of infighting with the additional reach of the Thai foot work. Or maybe you're a boxer and you need to add some groundwork to your arsenal, time to study Jiu-Jitsu.
The goal of Mixed Martial Arts is to produce a functional, evolving, and most importantly well rounded style that can be used effectively and consistently in a variety of situations. This is grand experiment has ridden on the back of very popular no holds barred tournaments such as the iconic "UFC" which probably had more than anything else to do with waking the nation up to the potential of mixing martial disciplines to develop the ultimate fighting style, and it in turn has increased the popularity of the matches.
Very few serious martial artists fence themselves in by studying one style of martial arts exclusively anymore; my sensei studied kenpo, jiu-jitsu and tai chi. The tai chi improved his blocking ability, as his slight stature made the hard blocks of kenpo and jiu-jitsu less effective.
The two styles that have proven most consistently effective in MMA have been Muay Thai and Brazilian Jiu-Jitsu. These styles complement each other perfectly.
Both being very effective in-fighting styles; with jiu-jitsu's brilliant grappling techniques and throws and Muay Thai's knees and elbows, either on the ground or standing. Muay Thai also gives added reach with strong kicks and some long distance attacks. Together they give the fighter full coverage, something to slip through every opening and counter every attack.
Thanks to the boom in popularity that martial arts saw with the release of Bruce Lee's films we now have many highly skilled homegrown martial artists with schools of mixed disciplines like Peak Performance Martial Arts in Keller, Texas , where you can begin your study of MMA or round out your existing education with instruction in some new styles.