Theseus is an extremely complex figure, the various stories attached to his name, some very old, some less so, are often difficult to reconcile. In this page I have tried to give a coherent resume! In some sources Theseus is son of the Athenian king Aigeus, elsewhere he is the son of Poseidon. Either way, his mother was Aithra, daughter of Pittheus of Troezen. According to Apollodoros and others, before leaving Troezen Aigeus left a sword and sandals under a rock telling Aithra that if he had a male child she should send him to Athens as soon as he was old enough to lift the rock. The early fifth-century lyric poet Bacchylides records the young Theseus' arrival at Athens in an Ode. On his way to Athens Theseus dealt with various beasts (like the Krommyonian Sow) and brigands (including Sinis, Prokroustes and Skiron). These labors and his arrival in Athens are recounted in Apollodoros and also in Bacchylides Ode 18. On arrival in Athens Theseus has to cope with the hostility of his new stepmother, Medea.
Theseus' voyage to Crete where he kills the Minotaur with the help of Ariadne follows. Bacchylides records how Minos challenged Theseus about his claim to be the son of Poseidon by throwing a ring into the sea for Theseus to retrieve, which he does. Theseus' underwater encounter with Amphitrite is depicted in vase-painting and told in Bacchylides, Ode 17. Having disposed of the Minotaur Theseus left for home with Ariadne whom he somehow lost on the way. The famous story of how Theseus forgot to change the black sails on his boat for white ones and Aigeus' suicide is late, perhaps an invention of the Roman period, possibly to explain the name of the Aegean sea. Theseus later married Ariadne's sister, Phaedra.
Theseus' claim to the throne of Athens was challenged by his cousins, the Pallantidai, but he defeated them. This event logically precedes Theseus' accession to the throne, but Euripides in the Hippolytos places it much later and makes Theseus' killing of a relative the motive for his temporary exile in Troezen.
Theseus' further adventures include the Centauromachy, in which he helped his Lapith friend Peirithoos. With Peirithoos he also made a trip to the Underworld in an attempt to kidnap Persephone, the pair also kidnapped the young Helen. Theseus also battled the Amazons. Sometimes, he accompanies Herakles on his expedition against them, sometimes the campaign is Theseus' alone. Either way, Theseus ended up with a captured Amazon wife, usually called Antiope but known as Hippolyte in the Hippolytos. This provoked an Amazon raid on Athens, mentioned in Aeschylus, Eumenides. Somehow, the captured Amazon was killed or returned to her people, leaving Theseus free to marry Ariadne's sister, Phaidra, whose story is told in the Hippolytos.
The earliest components of the Theseus myths seem to be the voyage to Crete and the escape with Ariadne, other adventures were gradually added, sometimes in order to make Theseus a hero comparable to Herakles. Plutarch, a Greek writer of the late 1st-early 2nd c. AD treated Theseus as the Athenian parallel to Romulus in his Life of Theseus and explained the similarity to Herakles by claiming that the young Theseus saw the older hero as a boy and wished to emulate him. The importance of Theseus can be to some extent explained by the desire of Athens to glorify their native hero. Thus Theseus (or his human father, Aigeus) often makes an appearance in tragedies set both in and outside Athens, like Euripides, Madness of Herakles, Medea; Sophocles, Oedipus at Colonus.
Bibliography
Kirk, The Nature of Greek Myths, pp. 152-6
Buxton, Imaginary Greece (see index)
F. Graf, Greek Mythology, pp. 136-40 on Theseus as Attic hero (see also Theseus in index)
K. Dowden, The Uses of Greek Mythology, pp. 144-6 (+ index)
W.B. Tyrrell, F.S. Brown, Athenian Myths and Institutions (NY and Oxford, 1991) Chapter 7 (Theseus and the Parthenon as Mythic Propaganda).