According to Homer, the Cyclopes have no ships, nor ship-wrights, nor other craftsman, and know nothing of agriculture. They have no regard for Zeus or the other gods, for the Cyclopes hold themselves to be "better far than they".Homer says that "godlike" Polyphemus, the son of Poseidon and the nymph Thoosa, the daughter of Phorcys, is the "greatest among all the Cyclopes". Homer describes Polyphemus as a shepherd who:

mingled not with others, but lived apart, with his heart set on lawlessness. For he was fashioned a wondrous monster, and was not like a man that lives by bread, but like a wooded peak of lofty mountains, which stands out to view alone, apart from the rest, ... [and as] a savage man that knew naught of justice or of law. Although Homer does not say explicitly that Polyphemus is one-eyed, for the account of his blinding to make sense he must be. If Homer meant for the other Cyclopes to be assumed (as they usually are) to be like Polyphemus, then they too will be one-eyed sons of Poseidon; however Homer says nothing explicit about either the parentage or appearance of the other Cyclopes. Euripides
The Hesiodic Cyclopes: makers of Zeus thunderbolts, the Homeric Cyclopes: brothers of Polyphemus, and the Cyclopean wall-builders, all figure in the plays of the fifth-century BC playwright Euripides. In his  play Alcestis, where we are told that the Cyclopes who forged Zeus thunderbolts, were killed by Apollo. The prologue of that play has Apollo explain:

House of Admetus!
They had a thunderbolt, which their hands had shaped, like the many that the Father hurls down from all over heaven upon earth, in part already polished, while part remained unfinished. Three shafts of twisted hail they had added to it, three of watery cloud, three of ruddy flame and the winged South Wind; now they were blending into the work terrifying flashes, noise, and fear, and wrath with pursuing flames. Elsewhere they were hurrying on for Mars a chariot and flying wheels, with which he stirs upmen and cities; and eagerly with golden scales of serpents were burnishing the awful aegis, armour of wrathful Pallas, the interwoven snakes, and on the breast of the goddess the Gorgon herself, with neck severed and eyes revolving. Apollodorus
The mythographer Apollodorus, gives an account of the Hesiodic Cyclopes similar to that of Hesiods, but with some differences, and additional details. According to Apollodorus, the Cyclopes were born after the Hundred-Handers, but before the Titans (unlike Hesiod who makes the Titans the eldest and the Hundred-Handers the youngest).Uranus bound the Hundred-Handers and the Cyclopes, and cast them all into Tartarus, "a gloomy place in Hades as far distant from earth as earth is distant from the sky." But the Titans are, apparently, allowed to remain free (unlike in Hesiod). When the Titans overthrew Uranus, they freed the Hundred-Handers and Cyclopes (unlike in Hesiod, where they apparently remained imprisoned), and made Cronus their sovereign.