Penelope's name is glossed by the lexicographer Hesychius as "some kind of bird" — today arbitrarily identified with the Eurasian wigeon — in which the element -elōps is a common Pre-Greek suffix for predatory animals. The semantic relation between the proper name and the gloss, however, remains unclear.

In folk etymology, Pēnelopē is typically understood to combine the Greek word pēnē ("weft") and ōps ("face"), a sense considered appropriate for a cunning weaver whose motivation is difficult to interpret. Robert S. P. Beekes believed the name to be Pre-Greek, related to pēnelops or pēnelōps.

Penelope is married to Odysseus (Ulysses in Roman mythology), king of Ithaca, and is the daughter of Icarius of Sparta and Periboea, with alternative sources naming Polycaste or Asterodia as her mother. She has one son with Odysseus, Telemachus, born just before Odysseus was called away to fight in the Trojan War. In one tradition her original name was Arnacia or Arnaea.

She waits twenty years for Odysseus's return, devising cunning strategies to delay marrying any of the 108 suitors, who are led by Antinous and include Agelaus, Amphinomus, Ctessippus, Demoptolemus, Elatus, Euryades, Eurymachus, and Peisander. When Odysseus at last returns, disguised as an old beggar, he finds that Penelope has remained faithful. Her most famous trick was to pretend to weave a burial shroud for Odysseus's elderly father Laertes, claiming she would choose a suitor once it was finished; every night for three years she undid part of the shroud, until the slave Melantho discovered the subterfuge and revealed it to the suitors.

Penelope's efforts to delay remarriage are often seen as a symbol of marital fidelity to Odysseus. Athena, however, wishes her to show herself to the suitors so as to set their hearts a-flutter and win her greater honor from her husband and her son, and Penelope eventually appears before them. The scholar Irene de Jong observed that Athena takes the initiative in redirecting the story: where mortal and divine motives usually align, here Athena wants Penelope to fan the suitors' desire and so be more esteemed by husband and son, while Penelope herself has no clear motive beyond an unprecedented impulse to meet the men she loathes and perhaps speak with Telemachus.

The philosophy historian Giulia Sissa offers an alternate reading in which Penelope entertains and even enjoys the suitors' attention. The Odyssey, on this view, allows room for an identity independent of her being Odysseus's wife: while awaiting his return she makes plans to handle her suitors while responding to her own desires, giving them the opportunity to demonstrate themselves as candidates for her attention. According to Sissa, Penelope "innovates" by responding in the same register to the men's desires, using seductive wiles of messages and promises and inviting them to prove their excellence in personal and physical terms, requiring that they match Odysseus's bodily strength.

Penelope is ambivalent — at times asking Artemis to kill her and apparently considering marrying one of the suitors. When the disguised Odysseus returns, she announces that whoever can string Odysseus's rigid bow and shoot an arrow through twelve axe heads may have her hand. This decision becomes the turning point of the plot, enabling the hero's predicted triumph. There is debate over whether Penelope recognizes Odysseus: since he would easily surpass every suitor in any test of masculine skill, she may have set the contest so that he could reveal his identity; alternatively, since only Odysseus (and perhaps Telemachus) can actually use the bow, she might simply be delaying the suitors further.

When the contest begins, none of the suitors can string the bow. Odysseus wins and proceeds to slaughter them — beginning with Antinous, whom he finds drinking from his cup — with the help of Telemachus, Athena, and the slaves Eumaeus the swineherd and Philoetius the cowherd. After Odysseus reveals himself in glory, following Athena's makeover, Penelope cannot believe her husband has truly returned, fearing it might be a god in disguise. She tests him by ordering the slave Eurycleia to move the bed in their bridal chamber; Odysseus protests, declaring that he built the bed himself with one leg fashioned from a living olive tree. Penelope finally accepts his identity — a moment that highlights their homophrosýnē ("like-mindedness"). Homer implies that Odysseus would afterward live a long and happy life with Penelope and Telemachus, ruling his kingdom wisely and with success.

Penelope appears in the lost Greek epic Telegony, attributed to Eugamon of Cyrene and written as a sequel to the Odyssey. In it, Odysseus has a son, Telegonus, by Circe; grown to maturity, Telegonus is sent to find his father but is shipwrecked on Ithaca by a storm and, in hunger, begins plundering it. Odysseus and Telemachus defend the city, and in the ensuing fight Telegonus accidentally kills his father with a lance tipped with a venomous stingray spine. On discovering his father's identity, Telegonus brings Telemachus and Penelope to Circe's island, where Athena orders Telemachus to marry Circe while Telegonus marries the widowed Penelope; after burying Odysseus, Circe makes the other three immortal. According to Hyginus, Penelope and Telegonus had a son named Italus, who in some accounts gave his name to Italy. This legend inspired Sophocles's lost tragedy Odysseus Acanthoplex.

In early sources such as Pindar, the parents of the god Pan are Apollo and Penelope. Herodotus, Cicero, Apollodorus, and Hyginus instead make Hermes and Penelope his parents. Pausanias records the story that Penelope had been unfaithful to Odysseus, who on his return banished her to Mantineia. In the fifth century AD Nonnus names Pan's mother as Penelope of Mantineia in Arcadia. Other sources report that Penelope slept with all 108 suitors in Odysseus's absence and so gave birth to Pan — a myth reflecting a folk etymology that equates Pan's name (Πάν) with the Greek word for "all" (πᾶν). The Odyssey carefully suppresses this variant tradition.

Penelope is recognizable across Greek and Roman works, from Attic vase paintings — the so-called Penelope Painter is identified by his representations of her — to Roman sculptures copying or improvising on classical Greek models. She is identified by her seated pose, her reflective gesture of leaning her cheek on her hand, and her protectively crossed legs, which reflect her long chastity during Odysseus's absence and form an unusual pose for any other figure.

Latin references to Penelope revolve around her sexual loyalty to the absent Odysseus, a quality that suited the marital ideals of Roman society and represented the tranquility of the worthy family. She is mentioned by many classical authors, including Plautus, Propertius, Horace, Ovid, Martial, and Statius. Her use in Latin texts provided the basis for her ongoing role in the Middle Ages and Renaissance as the model of a chaste wife — a reputation reinforced when Saint Jerome named her among the pagan women famed for their chastity.