The ancient Greeks appropriated from Egypt and the Near East the basic techniques of dividing the night and day into hours by watching stars, shadows, and the flow of water, and transformed them into displays of cosmology, mathematics, and mechanical ingenuity. The fundamental concept behind Greco-Roman timekeeping was geometry in motion: the spherical heavens revolving with constant speed around the spherical Earth, while the Sun travels more slowly through the stars along its own circular orbit. The most familiar instrument for telling time, the sundial, was designed to be a projection of the spherical cosmos, guaranteeing that every hour of the day was equal and correct for the season and for one's location on the Earth. The mechanical water clock showed how mundane matter could be made to imitate the regularity of the heavenly bodies, producing a moving image of the sky. The objects illustrating this lecture will include elegant and sophisticated sundials of several designs, and the much scarcer remains of water-driven devices.