In Homer's Odyssey, Penelópē (Πηνελόπεια/Πηνελόπη) is the faithful wife of Odysseus, who keeps her suitors at bay in his long absence and so is eventually rejoined with him. Prior to recent readings, her name had been associated with faithfulness, but the most recent readings offer a more ambiguous interpretation.
The origin of her name is Pre-Greek and is more likely related to the Hesychius' gloss πηνέλοψ/*πηνέλωψ "some kind of bird" (arbitrarily identified today with Eurasian Wigeon), where -έλωψ is a common Pre-Greek suffix for predatory animals , however the semantic relation between the proper name and the gloss is not clear (Penelope was also the name of a bird-like ancient deity). In folk etymology, Πηνελόπη is usually understood to combine the Greek word for "web" or "woof" (πήνη / pene), and the word for "eye" or "face" (ὤψ / ōps), which is considered the most appropriate for a weaver of cunning whose motivation is hard to decipher, or alternatively πήνη and λέπω "peel, skive" (akin to leper) due to the shroud-unbraiding part of her myth.
On Odysseus's return, disguised as an old beggar, he finds that Penelope has remained faithful. She has devised tricks to delay her suitors, one of which is to pretend to be weaving a burial shroud for Odysseus's elderly father Laertes and claiming that she will choose a suitor when she has finished. Every night for three years, she undoes part of the shroud, until some unfaithful maidens discover her chicanery and reveal it to the suitors.
Because of her efforts to put off remarriage, Penelope is often seen as a symbol of connubial fidelity. Although we are reminded several times of her fidelity, Penelope does begin to become restless (due in part to Athena's meddling) and longs to "display herself to her suitors, fan their hearts, inflame them more" (xviii.183-84). She is ambivalent, variously calling out for Artemis to kill her and, apparently, considering marrying one of the suitors. When the disguised Odysseus returns, she announces in her long interview with the disguised hero that whoever can string Odysseus's rigid bow and shoot an arrow through twelve axe shafts may have her hand. "For the plot of the Odyssey, of course, her decision is the turning point, the move that makes possible the long-predicted triumph of the returning hero".
There is debate over the extent to which she is aware that Odysseus is behind the disguise. To Penelope and the suitors' knowledge, Odysseus (were he in fact present) would easily surpass all in any test of masculine skill. Since Odysseus seems to be the only person (perhaps excepting Telemachus) who can actually use the bow, it could merely have been another delaying tactic of Penelope's.
When the contest of the bow begins, none of the suitors are able to string the bow, except of course Odysseus, who wins the contest. Having done so, he proceeds to slaughter the suitors with help from Telemachus, Athena and two servants, Eumaeus the swineherd and Philoetius the cowherd. Odysseus has now revealed himself in all his glory, and it is standard (in terms of a recognition scene) for all to recognize him and be happy. Penelope, however, cannot believe that her husband has really returned—she fears that it is perhaps some god in disguise as Odysseus, as was the case in the story of Alcmene—and tests him by ordering her servant Euryclea to move the bed in their wedding-chamber. Odysseus protests that this cannot be done since he made the bed himself and knows that one of its legs is a living olive tree. Penelope finally accepts that he truly is her husband, a moment that highlights their homophrosyne (like-mindedness).
In one story of the Epic Cycle, subsequent to Odysseus' death, Penelope marries his son by Circe, Telegonus, with whom she becomes the mother of Italus. Telemachus also marries Circe when Penelope and Telemachus bring Odysseus's body to Aeaea.