There are two distinct groups of Cyclopes. In Hesiod's Theogony, Zeus releases the Cyclopes, the sons of Uranus and Gaia, from Tartarus, and receives his characteristic weapon, the thunderbolt, from them; in one of the most famous passages of Homer's Odyssey, the hero Odysseus encounters the Cyclops Polyphemus, the son of Poseidon and Thoosa, who lives with his fellow Cyclopes in a distant country. The connection between the two groups has been debated in antiquity and by modern scholars.As Robert Mondi says: "Why is there such a discrepancy between the nature of the Homeric Cyclopes and the nature of those found in Hesiod's Theogony? Ancient commentators were so exercised by this problem that they supposed there to be more than one type of Cyclops, and we must agree that, on the surface at least, these two groups could hardly have less in common." (R. Mondi, 1983. "The Homeric Cyclopes: Folktale, Tradition, and Theme," Transactions of the American Philological Association 113 (1983), pp. 17-18.)

Hesiod's Cyclopes