  We discuss experiments and observations aimed at testing the possible
space-time variability of fundamental physical constants, predicted by the
modern theory. Specifically, we consider two of the dimensionless physical
parameters which are important for atomic and molecular physics: the
fine-structure constant and the electron-to-proton mass ratio. We review the
current status of such experiments and critically analyze recent claims of a
detection of the variability of the fine-structure constant on the cosmological
time scale. We stress that such a detection remains to be checked by future
experiments and observations. The tightest of the firmly established upper
limits read that the considered constants could not vary by more than 0.015% on
the scale of 10 Gigayears.
