Over time, two more reindeer have been added: Rudolph and Robbie, the former a well known name due to the popular Christmas song Rudolph the Red-Nosed Reindeer, the latter a media character.
Also, another "reindeer" has shown up. A dog known as Olive the Other Reindeer showed on a Christmas TV special in 1999. Olive thought she was another reindeer (see below).
According to Moore's poem, the appearance is a "miniature sleigh, and eight tiny reindeer" and they are "more rapid than eagles". Moore himself does not describe them, nor their positions in the sleigh-team, but does say they fly. 
In some countries, such as Finland, Santa's reindeer do not fly.
- The original eight reindeer are drawn from the 1823 poem by Moore.
- Rudolph was added following the publication of Robert L. May's Christmas story in 1939
- Robbie was added by BBC television in aid of Comic Relief, around 1999.
The original eight reindeer are arranged as follows on Santa's sleigh:
Front Dancer Dasher Vixen Prancer Cupid Comet Blitzen Donner
The reindeer on the left are all female, those on the right are all male.
- Dasher - The first reindeer and the right-hand leader of the sleigh before Rudolph was included. He is the speediest reindeer.
- Dancer - The second reindeer and the left leader before Rudolph was included. She is the graceful reindeer.
- Prancer - The third reindeer and on the right in the second row. He is the most powerful reindeer.
- Vixen - The fourth reindeer and on the left-hand side in the second row. She is beautiful, and also powerful like her companion Prancer.
- Comet - The fifth reindeer and on the right-hand side in the third row. He brings wonder and happiness to children when Santa flies over everyone's houses.
- Cupid - The sixth reindeer and on the left-hand side in the third row. She brings love and joy to children when Santa flies over everyone's houses.
- Donner - The seventh reindeer and on the right-hand side in the fourth row. He is the "thunder" reindeer.
- Blitzen - The eighth reindeer and on the left-hand side in the fourth row. She is the "lightning" reindeer.
Meaning of names
Donner and Blitzen mean thunder and lightning respectively.
Some have suggested that Donner's name is actually Donder which means thunder in Dutch and German. Some have speculated that Moore named Donner (thunder) in reference to Thor, the Norse God of Thunder.
Blitzen's name is derived from German Blitze which means lightning. Some have suggested that her name is actually Bliksem which is Dutch for lightning. Blitzen was named for lightning to go with Donner who was named for thunder.
- (Source: )
In An American Anthology, 1787–1900, Edmund Clarence Stedman reprints the Moore version of the poem, including the German spelling of "Donder and Blitzen", rather than the earlier Dutch version from 1823, "Dunder and Blixem". Both phrases translate as "Thunder and Lightning" in English, though the German word for thunder is actually "Donner", and the Dutch words would nowadays be "Donder en Bliksem".
Additional reindeer since the writing of the poem
Rudolph (the red-nosed reindeer)
Rudolph's story was originally written in verse by Robert L. May for the Montgomery Ward chain of department stores in 1939 and published as a book to be given to children in the store at Christmas time.
According to this story, Rudolph was the son of Donner, and was born with a glowing red nose, which made him a social outcast among the other reindeer. However, one Christmas eve it was too foggy for Santa Claus to make his flight around the world. About to cancel, Santa suddenly noticed Rudolph's nose, and decided it could be a makeshift lamp to guide his sleigh. Since then Rudolph has been said to be a permanent member of Santa's team, and leads them on their way.
Rudolph's story is a popular Christmas story that has been retold in numerous forms including a popular song, a television special, and even a feature film.
Robbie (Rudolph's son)
Robbie was an animated BBC Christmas comedy television special created in aid of the charity Comic Relief.
Olive, the Other Reindeer
Although not actually a reindeer, Olive is a fictional dog who believes she might be a reindeer. In Matt Groening's 1999 Christmas special Olive, the Other Reindeer, the new character is added to the team to lead Santa's sleigh, at least temporarily. The name is a reference to the phonetic sound of the phrase, "All of the other reindeer."