Atomic Clocks, Toward 10^-18 Accuracy

Atomic transition frequencies have become the most accurately measured physical quantities, which has led to the second being defined based on the hyperfine transition frequency of 133Cs since 1967. Recently, optical clocks based on the narrow optical transitions of a single ion in a Paul trap or neutral atoms in an optical lattice have shown their capabilities to surpass the best microwave clocks, and some of them have already reached uncertainty levels below 10^-17. Optical clocks, due to their ultimate accuracy, will serve not only to provide a new definition of the second but also to probe temporal variations of fundamental constants such as the fine structure constant and of the couplings of fundamental constants to forces like gravity. In this talk the fundamental aspects, current performance, and the applications of atomic clocks are reviewed.