Polyphemus was localized in antiquity on the east side of Sicily, near Aetna. At some point Aetna was conceived of as a natural forge for Cyclopes helping Hephaestus/Vulcan make lightning and thunder for Zeus. This would be the Hesiodic kind of Cyclopes, not the Homeric kind, who are portrayed as an exotic tribe of humans (for the various types of ancient Cyclopes, cf. R. Mondi, ‘The Homeric Cyclopes: Folktale, Tradition, and Theme,” TAPA 113 (1983) and R. Buxton, ‘Landscapes of the Cyclopes’ in G. Hawes [ed.] Myths on the Map ). As Pliny at least indicates, offshore volcanic rocks north of Catania near Acitrezza were equated with the rocks hurled by Polyphemus at the escaping Greeks. Nearby is a small island, very close to the shore, called Lachea, apparently after the obscure adjective λάχεια (or is it a proper noun?) that describes the island offshore of the land of Cyclopes in Book 9 of the Odyssey (conventionally called “Goat Island”). Cluver in the early 17th c. argued that the Egadi off of Trapani on the west side of Sicily provided a more appropriate “Goat Island,” a hypothesis developed at length by Samuel Butler in the late 19th c. (see further the section ‘Modern Localization’ on this site).
Thucydides, History of the Peloponnesian War, 6.2.1
Euripides, Cyclops 20 (cf. 62, 95)
“SILENUS. And as we were rounding Cape Malea, an east wind blew down on the ship  and cast us to land near this crag of Aetna, where Neptune’s one-eyed sons, the man-slaying Cyclopes, dwell in their remote caves.”
(online text: Eng., Grk.)
Theocritus, Idyll 11.7
Virgil, Aeneid 3.571
Ovid, Metamorphoses 14.154ff.
Pliny the Elder, Natural History 3.38
Statius, Thebaid 6.716
Dictys Chronicle of the Trojan War 6.5
“Then they had gone to the island of Sicily, where the brothers Cyclops and Laestrygon had treated them with every indignity and where Polyphemus and Antiphates, who were the sons of the former, had killed many of them.”
(online text: Eng.)
“Riviera of the Cyclopes”, east Sicily
(photos J. S. Burgess)