Phaidra, Prokris, and Ariadne are all logically named together in Homer’s v. 321 of Book Eleven, since all three pertain particularly to the mythology of Athens. Of the three, Homer mentions only Ariadne’s misadventure on the island of Naxos on her way with Theseus from Crete to Athens; he tells nothing of the well-known ancient stories about Phaidra and Prokris. Phaidra’s tale is told by Apollodoros in his Library:
Theseus joined Hercules in his expedition against the Amazons and carried off Antiope, or, as some say, Melanippe; but Simonides calls her Hippolyte. Wherefore the Amazons marched against Athens, and having taken up a position about the Areopagus they were vanquished by the Athenians under Theseus. And though he had a son Hippolytus by the Amazon, Theseus afterwards received from Deucalion in marriage Phaedra, daughter of Minos; and when her marriage was being celebrated, the Amazon that had before been married to him appeared in arms with her Amazons, and threatened to kill the assembled guests. But they hastily closed the doors and killed her. However, some say that she was slain in battle by Theseus.
And Phaedra, after she had borne two children, Acamas and Demophon, to Theseus, fell in love with the son he had by the Amazon, to wit, Hippolytus, and besought him to lie with her. Howbeit, he fled from her embraces, because he hated all women. But Phaedra, fearing that he might accuse her to his father, cleft open the doors of her bedchamber, rent her garments, and falsely charged Hippolytus with an assault. Theseus believed her and prayed to Poseidon that Hippolytus might perish. So, when Hippolytus was riding in his chariot and driving beside the sea, Poseidon sent up a bull from the surf, and the horses were frightened, the chariot dashed in pieces, and Hippolytus, entangled in the reins, was dragged to death. And when her passion was made public, Phaedra hanged herself.
Pausanias tells only a little more in his Hellados Periegesis (Description of Greece, I xxii 2):
Everybody, even a foreigner who has learnt Greek, knows about the love of Phaedra and the wickedness the nurse dared commit to serve her. The Troezenians too [i.e., like the Athenians] have a grave of Hippolytus, and their legend about it is this. When Theseus was about to marry Phaedra, not wishing, should he have children, Hippolytus either to be their subject or to be king in their stead, sent him to Pittheus to be brought up and to be the future king of Troezen. Afterwards Pallas and his sons rebelled against Theseus. After putting them to death he went to Troezen for purification, and Phaedra first saw Hippolytus there. Falling in love with him, she contrived the plot for his death. The Troezenians have a myrtle with every one of its leaves pierced. They say that it did not grow originally in this fashion, the holes being due to Phaedra’s disgust with love and to the pin which she wore in her hair.