Being a granddaughter of Poseidon, Catullus (64. 28) calls her Neptunine. As a marine divinity, she dwelt like her sisters, the Nereids, in the depth of the sea, with her father Nereus. She there received Dionysus on his flight from Lycurgus, and the god, in his gratitude, presented her with a golden urn.
When Hephaestus was thrown down from heaven, he was likewise received by Thetis.
Poseidon and Zeus himself are said by some to have sued for her hand, but when Themis declared that the son of Thetis would be more illustrious than his father, both suitors desisted.
Others state that Thetis rejected the offers of Zeus, because she had been brought up by Hera and the god, to revenge himself, decreed that she should marry a mortal. Cheiron then informed his friend Peleus how he might gain possession of her, even if she should metamorphose herself; for Thetis, like Proteus, had the power of assuming any form she pleased, and she had recourse to this means of escaping from Peleus, but the latter did not let her go, until she again assumed her proper form.
Others again relate that a marine divinity appeared to Peleus on Mount Pelion, and testified her love to him, but without revealing herself to him. Peleus, however, who saw her playing with dolphins, recognised the goddess, and henceforth shunned her presence. But she encouraged him, reminding him of the love of Eos to Tithonus, of Aphrodite to Anchises, etc, and promised to present him with a son who should be more illustrious than any mortal.
The wedding of Peleus was honoured with the presence of all the gods. After she had become the mother of Achilles, she bestowed upon him the tenderest care and love.
Thetis had a temple (Thetideion) between Old and New Pharsalus in Thessaly, and in Sparta and Messenia she was likewise worshipped.
From The Theogony of Hesiod
(ll. 240-264) And of Nereus and rich-haired Doris, daughter of Oceanus the perfect river, were born children, passing lovely amongst goddesses, Ploto, Eucrante, Sao, and Amphitrite, and Eudora, and Thetis, Galene and Glauce, Cymothoe, Speo, Thoe and lovely Halie, and Pasithea, and Erato, and rosy-armed Eunice, and gracious Melite, and Eulimene, and Agaue, Doto, Proto, Pherusa, and Dynamene, and Nisaea, and Actaea, and Protomedea, Doris, Panopea, and comely Galatea, and lovely Hippothoe, and rosy-armed Hipponoe, and Cymodoce who with Cymatolege and Amphitrite easily calms the waves upon the misty sea and the blasts of raging winds, and Cymo, and Eione, and rich-crowned Alimede, and Glauconome, fond of laughter, and Pontoporea, Leagore, Euagore, and Laomedea, and Polynoe, and Autonoe, and Lysianassa, and Euarne, lovely of shape and without blemish of form, and Psamathe of charming figure and divine Menippe, Neso, Eupompe, Themisto, Pronoe, and Nemertes who has the nature of her deathless father. These fifty daughters sprang from blameless Nereus, skilled in excellent crafts.