Experimental techniques of laser cooling and trapping, along with other cooling techniques, have produced gaseous samples of atoms so cold that they are, for many practical purposes, in the quantum ground state of their centre-of-mass motion. Such low velocities have virtually eliminated effects such as Doppler shifts, relativistic time dilation and observation-time broadening that previously limited the performance of atomic frequency standards. Today, the best laser-cooled, caesium atomic fountain, microwave frequency standards realize the International System of Units (SI) definition of the second to a relative accuracy of ≈3×10
−16
. Optical frequency standards, which do not realize the SI second, have even better performance: cold neutral atoms trapped in optical lattices now yield relative systematic uncertainties of ≈1×10
−16
, whereas cold-trapped ions have systematic uncertainties of 9×10
−18
. We will discuss the current limitations in the performance of neutral atom atomic frequency standards and prospects for the future.