  We discuss the usage of measurements of the stability of nature's fundamental
constants coming from comparisons between atomic clocks as a means to constrain
coupled variations of these constants in a broad class of unification
scenarios. After introducing the phenomenology of these models we provide
updated constraints, based on a global analysis of the latest experimental
results. We obtain null results for the proton-to-electron mass ratio
${\dot\mu}/{\mu}=(0.68\pm5.79)\ti mes10^{-16}\, {\rm yr}{}^{-1}$ and for the
gyromagnetic factor ${\dot g_p}/{g_p} =(-0.72\pm0.89)\times10^{-16}\, {\rm
yr}{}^{-1}$ (both of these being at the 95 % confidence level). These results
are compatible with theoretical expectations on unification scenarios, but much
freedom exists due to the presence of a degeneracy direction in the relevant
parameter space.
