Class 1 consists of the Giants as primitively conceived, creatures of human form so huge that after the defeat of their attack on the gods they were buried under islands, Enceladus for instance under Sicily, and Polybotes under Cos; while Tityus in Hades covered nine roods of ground. But in course of time, to differentiate them from gods and heroes, their attributes became more terrific and they passed into classes 2 and 3. Giants, in the traditions of various races, were the personifications of violent forces of nature, such as volcanoes.
Class 2 includes such monsters as the Hecatoncheires (the Hundred-handed Giants); the three Graiae, having only one eye and one tooth between them; the Cyclopes, with a single eye apiece; the Medusa with her huge and hideous head and petrifying eyes; Argus, with eyes all over his body.
Class 3 embraces a very large number of monsters: the Giants, as later represented, with their legs terminating in serpents; Cecrops and Erechtheus, whose bodies also terminated in serpents; Typhoeus, a particularly terrible creature, with a hundred serpents’ heads; Echidna, with the head and bust of a young woman, the rest a serpent; the Arcadian Satyrs, goat-footed with horns and tail, and the Anatolian Satyrs with the ears, feet and tail of a horse. The Sphinx of the dramatic poets is a winged woman with the body of a dog or lion; she was derived probably not from Egypt, but from Chaldea. Scylla, a marine monster, had, according to Homer, twelve dangling feet, six long necks and a hideous head on each, with three rows of teeth, the body lying concealed in a cavern. The idea was perhaps derived from some kind of squid. Later she was given a more human form: Virgil describes her as having the body of a young woman, the tail of a dolphin, and a girdle of dogs’ heads. The Tritons were monsters combining a human body with a fish’s tail. The Centaurs had a human body, rising from the body and legs of a horse; in primitive representations the front legs are those of a man. The Minotaur had a human body with the head of a bull... Two types of monster, the Sirens and the Harpies, joined a woman’s head to the body of a bird, a widespread fantasy found in fables in all parts of the world. The Harpies were primitively represented as women with birds’ wings, later as birds with women’s heads.
In class 4 may be included the Dragons, though the dragon (Gk. drakon, L. draco) is not properly a monster at all, but merely a large serpent. It figured frequently as the guardian of shrines (e.g. the Python at Delphi slain by Apollo), as an attribute of Asclepius, or as a genius loci. But dragons were sometimes given monstrous peculiarities, such as wings or additional heads. Winged dragons drew the cars [chariots] of Triptolemus and Medea. Fire-breathing dragons are especially a product of Christian art. In the same class we have such monsters as Cerberus, with his three heads and hair composed of snakes; the Chimaera, combining the head of a lion, the body of a goat and a tail ending in a serpent’s head; and the Griffin, part eagle and part lion (see Tenniel’s illustration of the Gryphon in ‘Alice in Wonderland’). The Griffins were first referred to, we are told, by Hesiod (in a lost passage); according to Herodotus they guarded the gold in Scythia. One of the strangest monsters is the Hippalectryon: it had the head and forelegs of a horse, and behind these the legs, tail and body of a rooster. There are extant representations of it on two vases by Nicosthenes, and it is mentioned by Aristophanes (Ran. 937-8), from whom we learn that it (as also the Tragelaphus or goat-stag) was copied from Persian sources. It is not surprising that so inelegant a conception disappeared before long from Greek art and finds no place in Greek myth. The Hippocampus was a horse with fish-like tail, on which the gods of the sea are often represented riding.
Monsters made little appeal to the Romans. In the comparatively rare cases where monsters figure in their literature (e.g. Scylla in the ‘Aeneid), it is generally in imitation of Greek models.
[From The Oxford Companion to Classical Literature]