  In this paper we discuss a possible cosmological time evolution of
fundamental constants from the theoretical and experimental point of views. On
the theoretical side, we explain that such a cosmological time evolution is
actually something very natural which can be described by mechanisms similar to
those used to explain cosmic inflation. We then discuss implications for grand
unified theories, showing that the unification condition of the gauge coupling
could evolve with cosmological time. Measurements of the electron-to-proton
mass ratio can test grand unified theories using low energy data. Following the
theoretical discussion, we review the current status of precision measurements
of fundamental constants and their potential cosmological time dependence.
