Commemorating the theft of fire from the Greek gods, a fire was kept burning throughout the original Olympic games. In the modern games a flame is transported from Greece to the various sites of the games as a symbol of the peace between the continents.
The Olympic torches are supposed to exemplify the national character of the host nation and, as such, they provide an interesting snapshot into the collective phyche of the host nations at a point in history.
For example, note the heavy traditional style torch used in the London games, also known as the austerity games. The first games after the second world war, it harks back to the traditions of the first Greek games. The modern Chinese torch, by comparison, is shaped like a traditional Chinese scroll, but replete with phoenix rising from the flames as if to proclaim the rise of a new china from the ashes of the old.
The New York Times is hosting an interactive slide show of every Olympic torch from the 1936 Berlin summer games, through to the current Beijing torch.