According to Clement Clarke Moore's poem "A Visit From St. Nicholas," the order of Santa's reindeer are Dasher, Dancer, Prancer and Vixen. The next four are Comet, Cupid, Donner and Blitzen. These last two were named Dunder and Blixem originally.
According to the booklet written by Robert L. May in 1939, a reindeer named Rudolph had a red nose that glowed brightly enough to lead Santa's sleigh and the other reindeer through a foggy Christmas Eve night.
Though tales of flying reindeer that pull Santa's sleigh are apocryphal, there are indeed real animals called reindeer. They are of the same species as caribou. The difference is that reindeer live in Europe and Eurasia, and caribou are found in North America and are wild. If a caribou is tamed, it becomes a reindeer.
The reindeer is unusual because both the male and female deer have antlers. In other species, only the male deer has antlers. The antlers of the reindeer are unusually showy, with snags, branchlets and points. Still, like other antlers, they are shed and regrown every year. Male reindeer lose their antlers each fall, but female reindeer retain them until the spring. Because of this, as the San Diego Zoo speculates, Santa's reindeer might be female.