Brazilian jiu jitsu, MMA and Kickboxing Brazilian Jiu-Jitsu ( or BJJ for short) is a martial art, combat sport, and a self defence system that focuses on grappling and especially ground fighting. Mixed Martial Arts (MMA), popularly known as cage fighting or ultimate fighting is a full contact combat sport that allows a wide variety of fighting techniques and skills, from a mixture of other combat sports, to be used in competitions. The rules allow the use of both striking as well as grappling techniques, both while standing and while on the ground.