Muay Thai specialises in the eight limbs. Fist, legs, knees and elbows.
Savate a french kickboxing art that uses point kicks in a fast manor.
Brazilian jiu jitsu - a ground fighting art which uses dominant positions, submissions, sweeps. Usually trained in a GI using chokes from the collar.
Submission wrestling - the use of takedowns and submissions for dominants. Clinch and and tye ups while standing is on the agenda for this art.
MMA - UFC comes to mind when you think of this. Using stand up strikes, clinch work, wrestling and finishing it of with Brazilian jiu jitsu or ground and pound. Very functional concept way of fighting.