Wherefore the daughters of Oceanus could not untroubled look upon them face to face nor endure the din in their ears. No shame to them! on those not even the daughters of the Blessed look without shuddering, though long past childhood’s years. But when any of the maidens doth disobedience to her mother, the mother calls the Cyclopes to her child—Arges or Steropes; and from within the house comes Hermes, stained with burnt ashes. And straightway he plays bogey to the child and she runs into her mother’s lap, with her hands upon her eyes. But thou, Maiden, even earlier, while yet but three years old, when Leto came bearing thee in her arms at the bidding of Hephaestus that he might give thee handsel and Brontes set thee on his stout knees—thou didst pluck the shaggy hair of his great breast and tear it out by force. And even unto this day the mid part of his breast remains hairless, even as when mange settles on a man’s temples and eats away the hair. And Artemis asks:

Cyclopes, for me too fashion ye a Cydonian bow and arrows and a hollow casket for my shafts; for I also am a child of Leto, even as Apollo. And if I with my bow shall slay some wild creature or monstrous beast, that shall the Cyclopes eat. Virgil
The first-century BC Roman poet Virgil seems to combine the Cyclopes of Hesiod with those of Homer, having them live alongside each other in the same part of Sicily.
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.