Satyrs appear predominantly in Greek Mythology as the followers of Dionysus. They are depicted in a number of ways, the most common being that of the upper half of a man and the lower half of a goat, sometimes possessing horns. They were less often depicted with the lower halves of horses. In either form, however, they possessed a long thick tail and constantly erect penis.
As time progressed they were depicted as 'more human' with less animalistic characteristics, until only the tail remained to show that they were satyrs.
See also the god Pan.