The offspring of the woman
The woman's offspring and the serpent's crushed head — a proto-messianic promise in Christian reading (with Revelation 12), or the ongoing enmity of humanity and snakes (the common Jewish reading, though the Targums also read a deliverer here).
Genesis 3:15
15I will put hostility between you and the woman, and between your offspring and her offspring. He will bruise your head, and you will bruise his heel.”
What each tradition says
Rabbinic / Midrashic
God puts enmity between the serpent and the woman, and between the serpent's seed and her sons' seed. If her sons keep the law, they will smite the serpent's head; if they forsake it, the serpent wounds their heel. They will have medicine, not the serpent; in the days of King Meshiha they will make a remedy for the heel.
Targum Jonathan ben Uzziel (Pseudo-Jonathan); trans. J. W. Etheridge (1862), The Targum of Jonathan ben Uzziel (trans. J. W. Etheridge, London, 1862) — Targum on Genesis 3:15
Patristic
Irenaeus says that from that time, the one who should be born of a woman—namely from the Virgin, after Adam's likeness—was preached as keeping watch for the serpent's head. He identifies this as the seed Paul mentions in Galatians, until whom the law of works was established and to whom the promise was made.
Irenaeus of Lyons (c. 130-c. 202), Against Heresies (trans. Alexander Roberts and William Rambaut), in Ante-Nicene Fathers, vol. 1 (Buffalo: Christian Literature Publishing Co., 1885) — Book V, ch. 21, §1
Catholic
Holweck reads Genesis 3:15 as the Proto-evangelium, the earliest gospel, placing enmity between the serpent and the woman. The Vulgate's "she" is interpretative and cannot be defended critically. The conqueror from the woman's seed who should crush the serpent's head is Christ, while the woman at enmity with the serpent is Mary.
Frederick Holweck (1856-1927), The Catholic Encyclopedia, vol. 7, s.v. 'Immaculate Conception' (New York: Robert Appleton Company, 1910) — Opening section, on the Proto-evangelium (Genesis 3:15)
Orthodox
St. Philaret teaches that in Genesis 3:15 God promised the woman’s seed would bruise the serpent’s head. He explains this means Jesus Christ would overcome the devil who deceived men and deliver them from sin, the curse, and death.
St. Philaret (Drozdov) of Moscow (1782-1867); trans. R. W. Blackmore (1845), The Longer Catechism of the Orthodox, Catholic, Eastern Church, in The Doctrine of the Russian Church (Aberdeen, 1845) — Questions 172-173 (on Genesis 3:15)
Reformed / Protestant
Calvin holds Moses' words are not ambiguous, but he disagrees with interpreters who take the seed as Christ, expecting someone from the woman's seed to wound the serpent's head. He would gladly support their opinion, but regards their reading of "seed" as too violently distorted.
John Calvin (1509-1564), Commentaries on the First Book of Moses Called Genesis, vol. 1 (trans. John King; Edinburgh: Calvin Translation Society, 1847) — Commentary on Genesis 3:15
Evangelical
John Wesley reads Genesis 3:15 as giving notice of three things concerning Christ. These are his incarnation as the seed of the woman, his sufferings and death pictured in Satan bruising his heel (his human nature), and his victory over Satan by that means.
John Wesley (1703-1791), Explanatory Notes upon the Old Testament (1765; CCEL's 'Wesley's Notes on the Bible') — Note on Genesis 3:15