Typhon and Echidna. Her name means 'throttler', from sphingo, 'to throttle': she asked a riddle of young Theban men who passed by the walls of the citadel where she was advantageously perched; if they could not answer it (and they usually could not), she strangled them.
Oedipus, however, found out the answer to her riddle and answered it correctly, whereupon the mortified Sphinx threw herself from the citadel and perished. (She had wings, but on this occasion was presumably too shocked to use them.)
In art the Sphinx is represented as having a woman's bust on the body of a lioness. This Greek Sphinx is quite distinct from the Egyptian sphinxes, which are the huge rock carvings in the desert (notably the one at Giza) of a lion with a Pharoah's head. These sphinxes pre-date the Greek one by several centuries.