For centuries, clocks have been used for navigation, an important application that continues today. The natural oscillations in atoms can provide standard references for accurate clocks because all atoms of a given element and isotope are exactly identical and because measurement uncertainties currently approach 1 part in 1018. At this level, many interesting effects, including those due to special and general relativity, must be calibrated and corrected for. I will give examples from clocks based on atomic ions but these are only representative of a world-wide effort to make better clocks based on both ions and neutral atoms.