Byblis was daughter of Miletus. Ancient authors name her mother variously as Tragasia daughter of Celaenus; Cyanee (Cyane) daughter of the river-god Maeander; or Eidothea daughter of King Eurytus of Caria. Her twin brother was Caunus. Nonnus instead makes Byblis, Caunus, and Miletus children of Asterius son of Minos — a rarer genealogy. This entry follows the Milesian twin of the incest-and-spring cycle.

In Ovid she first tries to excuse her desire as natural, then writes Caunus a long letter citing divine incest as precedent. Disgusted, he flees. She tears her clothes, runs mad, and pursues him through Greece and Asia Minor until exhaustion and endless tears transform her into a spring.

Parthenius cites a version close to Ovid that ends with Byblis hanging herself by her girdle, and another in which Caunus initiates the passion and then leaves before he loses control; Byblis still hangs herself after a long search. Conon follows that Caunus-first strand. Antoninus Liberalis has her refuse other suitors and leap from a cliff; hamadryads save her, put her to sleep, and change her into a nymph. Nonnus reverses the chase: Caunus courts Byblis with a song of divine incest. All traditions mention a spring born of her tears; Pausanias knew the spring Biblis in Milesian land.

Stephanus of Byzantium records the belief that Phoenician Byblos took its name from Byblis. Early modern sculpture recycled the theme: Pierre Le Gros the Younger's inventive restoration of a fragmentary Amor and Psyche group as Caunus rejecting Byblis spawned drawings and marbles, notably Laurent Delvaux's versions. The story stands beside Myrrha as a classical incest exemplum in Ovid's warning register.