The general character of centaurs is that of wild, lawless and inhospitable beings, the slaves of their animal passions. Two exceptions to this rule were Pholus and Chiron, who expressed their "good" nature, wise and kind centaurs. They are variously explained by a fancied resemblance to the shapes of clouds, or as spirits of the rushing mountain torrents or winds.

Dwelling in the mountains of Thessaly, the centaurs were the offspring of Ixion and Nephele, the rain-cloud. Alternatively, the centaurs were the offspring of Kentauros (the son of Ixion and Nephele) and some Magnesian mares or of Apollo and Hebe. It was sometimes said that Ixion planned to have sex with Hera but Zeus prevented it by fashioning a cloud in the shape of Hera. Since Ixion is usually considered the ancestor of the centaurs, they may be referred to by poets as the Ixionidae.

The Centaurs are best known for their fight with the Lapithae, caused by their attempt to carry off Hippodamia (a "horse" woman herself) on the day of her marriage to Peirithous, king of the Lapithae, himself the son of Ixion. The strife among these cousins is a metaphor for the conflict between the lower appetites and civilized behavior in humankind. Theseus, who happened to be present, a hero and founder of cities, threw the balance in favor of the right order of things, and assisted Pirithous. The Centaurs were driven off. Vignettes of the battle between Lapiths and Centaurs were sculpted in bas-relief on the frieze of the Parthenon, which was dedicated to wise Athena.

Like the Titanomachy, the defeat of the Titans by the Olympian gods, the contests with the Centaurs typify the struggle between civilization and barbarism.

Among the centaurs, the third one with an individual identity is Nessus. The mythological episode of the centaur Nessus carrying off Deianira, the bride of Heracles, also provided Giambologna (1529-1608), a Flemish sculptor whose career was spent in Italy, splendid opportunities to devise compositions with two forms in violent interaction. He made several versions of Nessus carrying off Deianira, represented by examples in the Louvre, the Grünes Gewölbe, Dresden, the Frick Collection, New York and the Huntington Library, San Marino, California. His followers, like Adriaen de Vries and Pietro Tacca, continued to make countless repetitions of the subject. When Belleuse tackled the same play of forms in the 19th century,  he titled it Abduction of Hippodameia .

In early Attic vase-paintings centaurs were represented as human beings in front, with the body and hind legs of a horse attached to the back; later, they were men only as far as the waist. The battle with the Lapithae, and the adventure of Heracles with Pholus are favourite subjects of Greek art.

Many centaur legends state that they are very fickle creatures, and often look to the sky to determine the fates. They are great astrologers and have a love for divination.