  We review recent progress in the study of varying constants and attempts to
explain the observed values of the fundamental physical constants. We describe
the variation of $G$ in Newtonian and relativistic scalar-tensor gravity
theories. We highlight the behaviour of the isotropic Friedmann solutions and
consider some striking features of primordial black hole formation and
evaporation if $G$ varies. We discuss attempts to explain the values of the
constants and show how we can incorporate the simultaneou s variations of
several 'constants' exactly by using higher-dimensional unified theories.
Finally, we describe some new observational limits on possible space or time
variations of the fine structure constant.
