Invited review article: The statistical modeling of atomic clocks and the design of time scales.

I will show how the statistical models that are used to describe the performance of atomic clocks are derived from their internal design. These statistical models form the basis for time scales, which are used to define international time scales such as International Atomic Time and Coordinated Universal Time. These international time scales are realized by ensembles of clocks at national laboratories such as the National Institute of Standards and Technology, and I will describe how ensembles of atomic clocks are characterized and managed.