Freestyle Kickboxing started in the US during the 1970's when American Karate practitioners became frustrated with strict controls on martial arts competitions that didn't allow full contact kicks & punches. Along with also facing Muay Thai Kickboxers in Muay Thai competition with very little success or becoming greatly injured from how hard the Muay Thai Kickboxers hit them & how more open Muay Thai was in regards to the strikes allowed in Muay Thai competitions compared to American Kickboxing competitions. Many questions were raised when the sport began about the high risk of injury to the competitors of these events. As a result, safety rules were improved & protective equipment was added to ensure competitor's safety and longevity in the sport. As this is a relatively new sport there are no long-term traditions. The sport has undergone changes & been refined during the last two decades because of Freestyle Kickboxers competing in other forms of Kickboxing like Shoot-Boxing, K1, & Full Contact Karate. Freestyle Kickboxing practitioners use sparring, punches, kicks, elbows, knees, clinching, throwing, takedowns, standing submissions, blocks, shadow boxing, & wood breaking that is learned & applied under professional instruction.
(Freestyle Kickboxing Information Provided from http://www.kickboxing.com/Styles/kickboxing.html)
The introduction of Jiu-jitsu to Brazil is largely credited to one Mitsuyo Maeda, who immigrated to Brazil in the 1920's & taught Jiu-jitsu to Carlos Gracie of Rio de Janeiro (more on the Gracies later). The large number of Japanese immigrants to South America (after all, the president of Peru is of Japanese ancestry) ensured that traditional Japanese martial arts, including Jiu-jitsu, would find a home in Latin America. However, Brazilian Jiu-jitsu evolved into its own distinct style, incorporating techniques honed in the rough favelas (shantytowns) of the big cities.
Brazilian Jiu-jitsu emphasizes ground fighting - in fact, most Brazilian Jiu-jitsu stylists want to take the fight to the ground, as opposed to the stand-up fighting of other fighting arts. Brazilian Jiu-jitsu practitioners believe that most fights end up on the ground, so you'd might as well learn the most effective ground fighting techniques available.
These techniques include the aptly named guard & mount. While these two techniques seem very simple, they form the foundation for almost all other Brazilian Jiu-jitsu techniques. Brazilian Jiu-jitsu really caught on with the advent of the Ultimate Fighting Championship (UFC) in 1993. The UFC, promoted by the Helio Gracie clan, was billed as the first tournament to pit practitioners of various martial arts against each other in an almost-no-holds-barred setting. The fact that Helio's son Royce won three of the first four tournaments using his family's brand of jiu-jitsu certainly cemented Brazilian Jiu-jitsu as an art demanding serious consideration. After almost 20 tournaments, the UFC has become a huge moneymaker, with cable pay-per-view revenues & fighting personalities rivaling those in professional wrestling.
No description of Brazilian Jiu-jitsu is complete without mentioning the Gracie family. Carlos Gracie, after learning Jiu-jitsu from Maeda, taught the art to his brothers Osvaldo, Gastão, Jorge, & Helio. The Gracie family, through challenge matches, televised tournaments, & sheer numbers, have spread their namesake style throughout the world. Some say that the Gracie clan is currently undergoing a Hatfield-&-McCoy style family feud, due to the incredible riches spawned by the current popularity of Brazilian Jiu-jitsu.
(Brazilian Jiu-jitsu Information Provided from http://www.kickboxing.com/Styles/BrazilianJiuJitsu.html)