  A number of positive and null results on the time variation of fundamental
constants have been reported. It is difficult to judge whether or not these
claims are mutually consistent, since the observable quantities depend on
several parameters, namely the coupling strengths and masses of particles. The
evolution of these coupling-parameters over cosmological history is also a
priori unknown. A direct comparison requires a relation between the couplings.
We explore several distinct scenarios based on unification of gauge couplings,
providing a representative (though not exhaustive) sample of such relations.
For each scenario we obtain a characteristic time dependence and discuss
whether a monotonic time evolution is allowed. For all scenarios, some
contradictions between different observations appear. We show how a clear
observational determination of non-zero variations would test the dominant
mechanism of varying couplings within unified theories.
