The ABC of Spanish style: The most popular style where matador kills a bull is spread over the Spain and Latin America. It is highly ritualized and has a lot of small details and traditions. In this kind of bullfighting there are three matadors (the main participants) each fighting two bulls. Each matador has five assistants. A matador should stop a running bull and keep it in the center of the ring as close as possible. Then two assistants on horses (picadors) stab the bull with lance. The aim is to weaken bull's neck and shoulder muscles, so letting the matador to kill the bull with a sword. Then three more assistants plant two colored sticks to the bull's flanks, which is further weakening of the beast. Then matador attracts the bull with the a red cap (red color is a tradition - bulls are color-blinded). There are different styles of bull pass. Finally, the matador kills a bull stabbing it with a sword between shoulder blades and through the heart.
The ABC of French style: In South France bullfighting became popular in 19th century, but the way the bullfighting done differs a lot. Before the fight an encierro (running) takes place: young men compete to outrun the charging bulls, which sometimes ends fatally for some men. Then the fight is held on small portable arenas: here a matador should snatch a rosettes and tassels off the bull in 15-20 minutes. Bulls are not killed in this kind of bullfighting.
The ABC of Portuguese style: Portuguese style is also bloodless. First a man on horse stabs a bull with three-four lances. Then a matador just with a cab simply plays with a bull. Then a group of eight men without any weapon challenge the bull directly. Bulls are not killed.
There are also some other kinds of bullfighting in Asia and Latin America, and of course rodeo in California.
The ABC of history: There are lots of theories, but usually they connect bullfighting with ancient Rome where people versus animal events were a warm-up for gladiators. Also religious motives can be seen as the bull is a symbol of most of ancient European and Asian cultures. They usually fought from horseback, and only in 18th century the fighting on foot was introduced.
Bullfighting is initially the show of courage and brave heartiness. The closer the bull to the matador the braver and more skilled he is considered to be. Sometimes bullfighting is called a sport though usually there is no competition.
Anti bullfighting campaigns: This performance for many centuries was a controversial one. Animal right campaigners widely protest against bullfighting as they suppose killing should not be done for entertainment. Another argument is that bulls are taking a slow and painful death. Bullfighting is banned in many countries, though bloodless variants are usually permitted. In Spain only Barcelona outlawed the bullfighting.
However, the bullfighting supporters object to the restrictions saying that these bulls are bred for the bullfighting and live well before they are killed living much better and freer before they are killed. Also they say that if it takes too much time to kill the bull, then the matador is considered low skilled.