An unusual range
Compared with the Iliad, the Odyssey is full of women, and they do a great deal. Penelope governs a household under siege for twenty years. Circe and Calypso are powers who detain the hero. Nausicaa makes the judgement that saves his life. Arete is supplicated in preference to her husband. Helen drugs the wine and tells her own version of Troy. Athena runs the plot. Eurycleia recognises him first. Anticleia explains the nature of death.
This is not a modern discovery. The poem's ancient readers noticed it, and Samuel Butler was moved by it to argue — with essentially no scholarly support, but not from nowhere — that the poem was written by a woman.
Penelope
The fullest characterisation. Her weapon is the same as her husband's: the shroud is mētis, using an obligation the suitors cannot refuse as a mechanism of delay. She extracts gifts from the men consuming her house. She sets the contest of the bow. And she tests the man who has just killed a hundred and eight people, refusing to accept him until he gives her a secret only two people know.
The test of the bed is the only occasion in the poem where anyone outmanoeuvres Odysseus.
Whether she recognises him before Book 23 is unresolved and probably unresolvable. See Penelope.
The powers
Circe and Calypso are both goddesses who detain him, and the poem's treatment of both is genuinely double. Calypso keeps him seven years while he weeps on the shore daily, and they sleep together in a formula that records no reluctance. Circe transforms his men into animals, and then, after an oath, becomes the most useful host in the poem.
Neither is a temptress in the later allegorical sense and neither is a victim in the modern sense. The poem holds captivity and intimacy together without resolving them, and modern retellings almost always resolve them one way or the other.
Nausicaa and Arete
Both exercise judgement that the plot depends on. Nausicaa decides, correctly, that a large naked stranger is a suppliant rather than a threat, and manages her own reputation while helping him. Arete is the person whose knees Odysseus is told to grasp, and her prominence has been discussed since antiquity as anomalous in Homer.
The limits
The poem's range should not be overstated, and its own text prevents overstating it.
In Book 1 Telemachus publicly orders his mother out of the hall and tells her that speech is the business of men. The Odyssey's most capable woman is sent upstairs by her adolescent son, and the poem records it as his first act of authority.
Twelve enslaved women are hanged in Book 22 for sexual relations with the suitors — relations they had no power to refuse. They are given a simile and no names except Melantho's.
Female slaves grind grain through the night; one of them, the weakest and last still working, prays for the suitors' last meal, and her prayer is taken as an omen. The poem notices her, and does not free her.
The Greek terms
Homophrosynē, like-mindedness between husband and wife, named in Book 6 as the greatest good there is. Kleos, fame — awarded to Penelope explicitly in Book 24, which is the poem's last statement on reputation and is about a woman. Dmōai, the enslaved women of the household.
Later interpretation
Twentieth- and twenty-first-century reception has concentrated on the figures the poem subordinates: Atwood's The Penelopiad gives the hanged women a chorus; Madeline Miller's Circe narrates from Aeaea. Emily Wilson's 2018 translation was widely discussed for its handling of the vocabulary applied to enslaved women. These are arguments with the poem conducted on the poem's own material.