Euterpe was born among the nine Muses, daughters of Zeus and Mnemosyne. Hesiod names the sisters Clio, Euterpe, Thalia, Melpomene, Terpsichore, Erato, Polyhymnia, Urania and Calliope. He does not yet divide the arts formally among them. Euterpe's later sphere of lyric poetry and music, and her characteristic aulos, belong to the later differentiation of the nine Muses in literature and art.

The aulos became Euterpe's familiar attribute in later art, but the instrument has its own mythology and should not be folded into a single story about the Muse. One famous cycle concerns Marsyas, who challenges Apollo to a musical contest and is brutally punished after losing. A separate story makes Pan compete with Apollo, with the mountain god Tmolus judging Apollo the winner; King Midas objects and receives ass's ears. The two contests are distinct traditions, even though later retellings sometimes blur them.

The Muses as a group are connected with the funeral of Achilles in the Odyssey. After Achilles has died, the nine Muses sing a lament for him while the Nereids mourn beside Thetis. The passage does not say Achilles died from an arrow in the heel, and it does not single Euterpe out from her sisters. Its importance for Euterpe is collective: music and lament belong to the power of the Muses together.

Pseudo-Apollodorus gives Euterpe a son, Rhesus, by the river god Strymon, while immediately noting that some authorities made Calliope his mother instead. Rhesus is the Thracian king whose late arrival at Troy ends in the night raid of Diomedes and Odysseus. Euterpe's motherhood of Rhesus is therefore a genuine ancient variant, but not the only surviving genealogy.

The Muses themselves were once challenged, and Euterpe stood among her sisters in the contest. Pierus, a king of Emathia in Thessaly, had nine daughters so gifted in song and so proud that they were called the Pierides after their father, and they boasted that their voices were the equal of the Muses of Olympus. The nine sisters accepted the challenge, and the contest was held on Mount Helicon, the mountain in Boeotia sacred to the Muses, before judges drawn from the nymphs of the land. The Pierides sang first, and they sang of the gods at their weakest, telling how the monster Typhon had once driven Zeus and all Olympus into hiding, and of a blessed world where mortals would be punished for nothing. It was skillful singing, but it was impious singing, and the judges frowned. Then the Muses rose one by one, and Calliope, the eldest of the nine, whose province was the great epics, sang the praises of the gods and the punishment of the wicked, and the victory went to the Muses. The Pierides, shrieking insults, were transformed on the spot into magpies, birds that chatter and scold forever, their beautiful voices gone to harsh noise. The story was the Muses' own warning: song was a divine gift, and to turn it against the gods was to lose it entirely.

The Greeks gave Euterpe and her sisters real soil and real sanctuaries. On Mount Helicon, in the Vale of the Muses, stood statues of the nine, and near them bubbled the spring of Hippocrene, the Horse's Spring, which the winged horse Pegasus had struck open with a blow of his hoof when the Muses tamed him. At Delphi on Mount Parnassus, where Apollo's oracle spoke, the Muses had their own altar beside the god they served as companions. In Athens, the groves of the Academy and the Lyceum, the city's great grounds for walking and teaching, were sacred to the Muses, and the philosopher Plato taught in the Academy near their shrine. The very word museum descends from the Greek mouseion, the shrine of the Muses, for a place where the Muses are honoured is a place where learning lives. When Roman poets took up Greek song, they called the Muses by their old Italian name, the Camenae, and the poet Vergil opened his epic of Aeneas, the Trojan prince whose wanderings were said to have founded Rome, by begging the Muse to tell him the causes of it all. Euterpe's image travelled with them, a young woman with a double pipe in her hands, delight standing ready to be summoned by any singer who began in the right way, with the goddesses invoked first.

Euterpe's name never left the world. In 1853 an English astronomer mapping the small planets of the solar system named one of them 27 Euterpe, a dark rock orbiting between Mars and Jupiter, so that the Muse of music circles the sun to this day. Botanists gave her name to a genus of slender palms of the South American rainforest, Euterpe oleracea and its kin, the trees that produce the purple açaí berry eaten around the world. Every museum on earth, every music hall where an orchestra tunes before a performance, every singer who warms up a voice, stands in a tradition that once began with an invocation to her and her eight sisters. She asked for no temples of gold and received the greatest one: the entire practice of music as a sacred art. From the foothills of Olympus to the night sky, Euterpe remains the Giver of Delight, the eternal answer to the question of why human beings sing at all.