Agenor's ancestry connects the Nile with the coast of Phoenicia. In Apollodorus's account, his father was Poseidon, the god of the sea, and his mother was Libya, daughter of Epaphus. Through Epaphus the family traced its descent to Io, the Argive woman whose wanderings brought her to Egypt. Agenor's brother Belus remained in Egypt and became the father of Aegyptus and Danaus, whose children would be drawn into the tragedy of the Danaid marriages. Agenor went to Phoenicia and established himself there. Traditions associate his kingship with Tyre or Sidon, but his story belongs to legendary genealogy rather than a securely documented royal chronology.

He married Telephassa, and together they raised the family at the centre of the search for Europa. Apollodorus names their daughter Europa and their sons Cadmus, Cilix and Phoenix. Cadmus would eventually found Thebes; Cilix was connected with the name Cilicia; Phoenix with Phoenicia. The genealogy was never entirely fixed. Some sources make Europa the daughter of Phoenix rather than Agenor, so that Agenor becomes her grandfather in that version. Thasus also joins the search in Apollodorus, but is there called a son of Poseidon or, in another account, of Cilix. These alternatives should not be combined into a single family tree in which every relationship is equally certain.

The defining moment of Agenor's story was the disappearance of Europa. Zeus desired her and approached in the form of a tame bull. When she mounted the animal, it carried her across the sea to Crete. There she bore Minos, Sarpedon and Rhadamanthys in the genealogy followed by Apollodorus, although the parentage and generation of Sarpedon vary between traditions. Europa later married Asterius, who brought up the children. Through Minos, the story leads towards the Cretan kingship, the Labyrinth and the Minotaur. For Agenor, however, the event began not as the foundation of a dynasty but as the unexplained loss of a daughter.

Agenor sent his sons to find Europa and forbade them to return without her. Telephassa went with the searchers. They failed to recover the missing princess, and Apollodorus describes them abandoning their return and settling in different places. Phoenix settled in Phoenicia; Cilix established himself near the river Pyramus, giving his name to Cilicia; Thasus founded a settlement on the island of Thasos. Cadmus and Telephassa reached Thrace. After his mother's death, Cadmus went to Delphi, where Apollo's oracle told him to stop searching for Europa and follow a cow. Where it lay down, he was to build a city. That journey led him to Boeotia and the foundation story of Thebes, including the dragon of Ares and the Spartoi who sprang from its sown teeth.

A much later version appears in the Chronography of John Malalas. There Agenor has a differently arranged household, and near the end of his life he orders the division of his lands among Phoenix, Syros and Cilix. Their territories receive the names Phoenicia, Syria and Cilicia. This is a separate explanatory tradition, not a missing final chapter that can simply be attached to Apollodorus's account of the unsuccessful search. Its interest lies in the same pattern: places and peoples are linked to members of a legendary royal family.

Agenor's importance survives through those family connections. Cadmus's descendants include Semele, mother of Dionysus, and the troubled royal house of Thebes; Europa's descendants connect the family with Crete. The stories do not show that Agenor's children literally created the civilisations of the Mediterranean. They show how Greek myth used kinship, journeys and lost relatives to connect communities across the sea. Agenor's command never brings Europa home, but the search gives his family a place in the remembered origins of many lands.