How is the Sphinx relevant to Greek mythology and what is the connection between the two?

Though the Sphinx itself is Egyptian in origin, the word 'sphinx' actually comes from the Greek word 'strangler', or 'female monster', which was applied to the Sphinx as it was incorporated into Greek mythology. The transportation of the Sphinx from Egypt to Greece probably had something to do with the strong trade links between the two civilisations.

There's only one Sphinx who actually appears in Greek mythology though, a daughter of Echidna, and she traditionally (as she does in Sophocles' play) guards the city of Thebes, posing her riddle. The actual riddle the Sphinx asked isn't recorded until Sophocles: a good example, actually, of the way the Greek dramatists take something from myth, place it in a dramatic setting, and then add to it at will!