A spear or sword is driven down in between the bull's shoulder blades straight down to its heart. This is a much easier target to kill a bull than trying to drive the sword or spear into the back of a bull's head.
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If your talking about the Spanish bull fighting. Yes, they would chase the bull around the ring teasing it, and making it tired each horsemen or the men on foot will attempt to spear the bull. (These spears are sharp and often colored brightly) Eventually they will give the bull the finishing blow. The bull will die and they normally get a horse or something that can pull the bull (with a rope that they have tied to it's legs, they then tie this to the harness of the other animal) they then pull the bull away.
Another answer:
In the traditional Spanish bullfight, the bull is killed during the bullfight. In Portugal, however, the bull is killed after the fight and out of the sight of the public.
There are two reasons:
1.) Killing the bull, at least in Spanish-style fights, is the aim of the fight but to be done in an exciting and artistic manner.
2.) A more practical reason the bull is killed is to prevent it from being 'recycled' or used again in another fight once the bull has healed. In a bullfight the bull has never encountered a man on foot all its life until it enters the ring. It thinks the cape is part of the man and attacks that. However, it quickly learns the cape is simply a lure and begins to go after the man. A 'recycled' bull would be extremely dangerous for the matador.
The matador kills using a slightly curved sword (estoque), not a spear. He has a small target slightly larger than a human fist that is directly behind the shoulder blades of the animal. If the sword hits the spot, it meets no resistance and severs a main artery near the heart. If not done properly it may puncture a lung and this is always met with booing from the fans. The reason the sword is curved is to cause more damage and kill the bull faster when he is forced, by waving the cape by a torero, to move his head back and forth.
To kill the bull properly the matador must go in directly over the horns and this is the most dangerous time for the man. It exposes the matador to a possible goring. Less honest matadores will try to move off to the side to kill the bull.
The great matador Manolete was killed by a bull in Linares, Spain, in 1947 as he went in over the horns for the kill. The goring severed his femoral artery in his leg.
However, he still hit the mark and the bull also died before Manolete could be carried to the infirmary.
Historically, spears were driven through the shoulder blades of the animal to kill it. A matador may also use a sword to deliver the final blow through the heart of the beast.