The story of Amalthea begins with a prophecy and a father's fear. Cronus, the Titan who had seized power from his own father Uranus, learned from Gaia, the earth-goddess, and Uranus, the sky, that he too would be overthrown by one of his children. To prevent this, he swallowed each child as his wife Rhea bore them: Hestia, Demeter, Hera, Hades, and Poseidon all disappeared into his belly. But when Rhea was pregnant with her sixth child, she devised a plan. She travelled to Crete and gave birth to Zeus in secret, in a cave on Mount Dicte, or in some accounts on Mount Ida. She wrapped a stone in swaddling clothes and presented it to Cronus, who swallowed it without looking, believing it to be the infant. Then she spirited the real child away to be hidden and raised in the Cretan mountains.

Zeus was entrusted to the nymphs Adrasteia and Ida, the daughters of Melisseus, the king of Crete, who became his foster-mothers. But the child needed milk, and for this the nymphs turned to Amalthea, a she-goat of extraordinary nature. In the earliest traditions Amalthea is the goat herself, a divine or semi-divine animal whose rich milk fed the future king of the gods. In later accounts, particularly those of the Roman poet Ovid, Amalthea is a naiad, a water nymph, who owned the goat that supplied the milk. Either way, the infant Zeus grew strong on her milk and on the honey brought by the bees of Crete, while the nymphs laid him in a cradle of gold. The poet Callimachus, writing in the third century BCE, describes the scene in his Hymn to Zeus: the Dictaean nymphs took the child in their arms, Adrasteia laid him in the golden cradle, and he sucked the rich teat of the she-goat Amalthea and ate the sweet honey-comb.

But milk alone could not keep the child hidden. Cronus had sharp ears and a sharper suspicion, and the wails of an infant god were not easily muffled. To drown out the baby's cries, Rhea summoned the Curetes, armed divine dancers who clashed their bronze shields and spears outside the cave, stamping their feet and shouting war cries so that the sound of battle would mask the sound of life within. The mythographer Apollodorus records that these armed guardians stood watch over the cave, banging their weapons against their shields to prevent Cronus from hearing the infant's voice. In some accounts the Corybantes, a similar band of ecstatic armed dancers, performed the same service. The noise was deafening, a wall of bronze and bronze that held back the end of the world.

As Zeus grew, his play became rougher, as the play of gods always does. One day, while tussling with Amalthea, he broke off one of her horns. The horn did not go to waste. Zeus, grateful for the nourishment she had given him, endowed the broken horn with magical power: whatever its bearer wished for, it would provide in endless abundance. This became the cornucopia, the horn of plenty, one of the most enduring symbols of abundance in Western art. In another version, recorded by Ovid in his Fasti, the goat's horn caught on a tree branch and snapped off, and the nymph Amalthea filled it with fresh fruits and herbs and presented it to the young god. The horn would later pass into the hands of heroes, and in some accounts Heracles himself received it as a gift.

When Amalthea the goat died, Zeus honoured her as only a god could. He took her hide and fashioned from it the aegis, his thunder-shield, a goatskin fringed with gold that he carried into battle and that would later pass to his daughter Athena, the goddess of wisdom and war. The very name aegis contains the Greek word for goat, aix, and the storm-shield was forever linked to the animal who had nursed its maker. Zeus also placed Amalthea among the stars as the constellation Capra, the goat that stands on the arm of Auriga the Charioteer in the northern sky. Her two kids, born at the very time she was nursing the infant god, were placed beside her as the Kids constellation, a trio of stars that have guided sailors and farmers for millennia. In some accounts a Golden Dog, placed by Rhea to guard the goat, was also given an immortal station. The goat who had fed a god became a god herself, in a way, her light still shining above the world she helped to save.