In Greek mythology and later Roman mythology, the Cyclopes ( sy-KLOH-peez; Greek: Κύκλωπες, Kýklōpes, "Circle-eyes" or "Round-eyes"; singular Cyclops  SY-klops; Κύκλωψ, Kýklōps) are giant one-eyed creatures. Three groups of Cyclopes can be distinguished. In Hesiods Theogony, the Cyclopes are the three brothers Brontes, Steropes, and Arges, who made for Zeus his weapon the thunderbolt. In Homers Odyssey, they are an uncivilized group of shepherds, the brethren of Polyphemus encountered by Odysseus. Cyclopes were also famous as the builders of the Cyclopean walls of Mycenae and Tiryns. In Cyclops, the fifth-century BC play by Euripides, a chorus of satyrs offers comic relief based on the encounter of Odysseus and Polyphemus. The third-century BC poet Callimachus makes the Hesiodic Cyclopes the assistants of smith-god Hephaestus; as does Virgil in the Latin epic Aeneid, where he seems to equate the Hesiodic and Homeric Cyclopes. From at least the fifth century BC, Cyclopes have been associated with the island of Sicily and the volcanic Aeolian Islands. Kinds
Three groups of Cyclopes can be distinguished: the Hesiodic, the Homeric and the wall-builders. In Hesiods Theogony, the Cyclopes are the three brothers: Brontes, Steropes, and Arges, sons of Uranus and Gaia, who made for Zeus his characteristic weapon, the thunderbolt. In Homers Odyssey, the Cyclopes are an uncivilized group of shepherds, one of whom, Polyphemus, the son of Poseidon, is encountered by Odysseus. Cyclopes were also said to have been the builders of the Cyclopean walls of Mycenae and Tiryns.
Abel proposed that fossil skulls of Pleistocene dwarf elephants, commonly found in coastal caves of Italy and Greece, may have given rise to the Polyphemus story. Abel suggested that the large, central nasal cavity (for the trunk) in the skull might have been interpreted as a large single eye-socket.Cyclopia, a rare birth defect, can result in foetuses which have a single eye. Although the possibility has been raised of a link between this deformity and the myth of the one-eyed Cyclopes, in such cases, the eye is below the nose—rather than above as in ancient Greek depictions.As noted above, Walter Burkert sees the possibility of the Hesiodic Cyclopes having ancient smith guilds as their basis. See also
Polyphemus § Possible origins, for stories of other cyclopian giants similar to the story of Polyphemus encounter with Odysseus
List of one-eyed creatures in mythology and fiction

Notes
References
Apollodorus, Apollodorus, The Library, with an English Translation by Sir James George Frazer, F.B.A., F.R.S. in 2 Volumes. Cambridge, Massachusetts, Harvard University Press; London, William Heinemann Ltd. 1921. Online version at the Perseus Digital Library. Bakker, Egbert J., The Meaning of Meat and the Structure of the Odyssey,  Cambridge University Press, 2013. ISBN 978-0-521-11120-1. Bremmer, J.N. (1987). Odysseus versus the Cyclops, in Myth and Symbol. The Norwegian Institute. Burkert, Walter (1982). Structure and History in Greek Mythology and Ritual. University of California Press. ISBN 978-0-520-04770-9. Burkert, Walter (1991). Greek Religion. Wiley-Blackwell. ISBN 978-0-631-15624-6. Caldwell, Richard, Hesiods Theogony, Focus Publishing/R. Pullins Company (1987). ISBN 978-0-941051-00-2.