  The idea of possible time or space variations of the `fundamental' constants
of nature, although not new, is only now beginning to be actively considered by
large numbers of researchers in the particle physics, cosmology and
astrophysics communities. This revival is mostly due to the claims of possible
detection of such variations, in various different contexts and by several
groups. Here, I present the current theoretical motivations and expectations
for such variations, review the current observational status, and discuss the
impact of a possible confirmation of these results in our views of cosmology
and physics as a whole.
