According to myths and legends, Theseus lived in the Late Bronze Age, about a generation (20–30 years) before the start of the Trojan War, which according to myth occurred at some time in the thirteenth century BCE.
In addition to his mythical heroic accomplishments, Theseus is considered the founder and king of ancient Athens and is responsible for the Synoikismos, the political unification of the twelve demes, the settlements or communities on the Attic peninsula of Greece, into the Athenian state.
The myths surrounding Theseus include his capture of the Marathonian Bull, his near-death at the hands of the sorceress Medea, his defeat of the Pallantidae Giants, his defeat of the Amazons and marriage to their Queen, Hippolyta (also known as Antiope), and his six labors—much like the twelve labors of Hercules—in which Theseus defeats and kills four brigands (robbers), one wrestler-king, and the Crommyonian Sow, a giant pig.
As a side note, shortly after returning to Athens, following his defeat of the Amazons, Theseus takes time from his busy heroic schedule to appear with Hippolyta in William Shakespeare's A Midsummer Night's Dream.
The most famous myth involving Theseus is his killing of the Minotaur, the fearsome, human-devouring half-man half-beast who lives in the inescapable Labyrinth on the island of Crete.
On his return voyage to Athens after killing the Minotaur, Theseus neglects to replace a black sail with a white sail as a signal to his father, Aegeus, King of Athens, that he's returned safely from the Minotaur. Aegeus, overcome with grief believing that Theseus has been killed, throws himself into the sea from the cliffs at Sounion, the southernmost point of the Attic peninsula, giving the Aegean Sea its name. As a result of his father's death, Theseus becomes King of Athens.
After another heroic adventure in which Theseus goes into the Underworld in a failed attempt to abduct Persephone, wife of Hades (after whom the Underworld is sometimes named), Theseus returns to Athens, where he is no longer welcome.
Facing rebellion in Athens, Theseus takes refuge on the island of Skyros, where Lycomedes, King of Skyros, kills Theseus by pushing him from the top of a cliff into the same sea in which Theseus's father, Aegeus, had thrown himself and died.