People in the Greco-Roman world lived according to a profusion of cycles of time ranging from a few days (e.g. series of markets in various towns) to multiple years (e.g. the Olympic festivals) in addition to the calendars that regulated their religious and other civic activities. In the cosmos too, the Sun, Moon, stars, and planets had disparate cycles governing their appearances and disappearances and motions. Astronomers sought ever-more-accurate measures of these cosmic periodicities and used them to bring orderliness into the operation of calendars and other social time cycles. Thinking in the longer term, they speculated whether all the heavenly bodies might return to their starting positions in some enormous "Great Year" comprising tens of thousands of ordinary years. This lecture will look at how ideas of cyclic time on the scale of days, months, years, and eons were represented visually through peg-board inscriptions, mechanical devices such as the Antikythera Mechanism, and imagery.