A satyr is a figure from Greek mythology. Satyrs were male companions of Pan and Dionysus who roamed the woods and mountains. Satyrs are often portrayed as males with strong bodily desires, wild, orgiastic and obsessed with drinking wine, music, dancing, and sex. They are after women (often the nymphs) and boys.
From the waist down Satyrs are goat-like, with furry goat’s legs, hoofs, and a tail. On their heads they have horns. Mature satyrs are often depicted in Roman art with goat’s horns, while boy satyrs are often shown with bony nubs on their foreheads.
The Romans connected their fauns (place-spirits of untamed woodland) with the Greek satyrs, which gave them a very similar appearance. Both the fauns, satyrs and Pan resemble the later depictions of the devil in Christian iconography.
Satyrs are often depicted in erotic or sexual situations, often with erections. They are a classical subject matter in erotic art. Occasionally they are also seen in BDSM type activities such as whipping or spanking women.
I am also working on putting together a blog with art on this subject by modern artists.