The Earth is not a good basis for precision timekeeping. Even though units of time are based on the Earth's rotation, it is known that it is unsteady and it is slowing down. When this discovery was made it was necessary to develop more accurate ways of keeping time. Atomic clocks were invented as a result of this need and have been refined to greater degrees of accuracy in an increasingly time-dependent world. This text presents the story of the development of atomic clocks and atomic timekeeping. It shows how and why reliable clocks were invented, how co-ordinated universal time was developed and how the needs for increased precision in the future is driving the refinement of atomic timekeeping to greater accuracy.