"Centauromachy" refers to the battle between the Centaurs and Lapiths of the Peneus Valley, in Thessaly.
In one story of the origins of these two related peoples, Centaurus and Lapithes are the twin sons of Apollo and a daughter of the river god Peneus. Centaurus mated with a mare to produce the first centaur. Lapithes became king of the Lapiths. One of his descendants was Ixion, the infamous king of the Lapiths. Ixion accidentally or intentionally killed his visiting father-in-law, making him the first man in the Greek mythological tradition to do in a relative.
Ixion was not through with his transgressions. When Zeus invited Ixion to Mt. Olympus, he violated guest-host relations once again, but from the guest's side this time. Ixion lusted after Zeus' wife, Hera. Before Ixion could attain his goal, Zeus found out and made a cloud resemble Hera to tempt the foolish mortal. Deceived, Ixion had intercourse with the cloud (which is given a name, Nephele), and became the progenitor of Centaurus or, more directly, of the centaurs themselves. After Zeus executed Ixion with his famous weapon, the thunderbolt, Ixion was attached permanently to a spinning, fiery wheel for all eternity in Tartarus.
A son (or stepson since Zeus is also named as father) of Ixion was Peirithoos, the good friend of Theseus.
The Centauromachy was fought at the wedding of the Lapith king Perithous (Peirithoos) and Hippodameia after the Centaurs, unused to alcohol, became intoxicated and tried to rape the bride. With the help of the Athenian hero Theseus, the Lapiths won the battle.