We consider astronomical and local bounds on the time variation of fundamental constants to test some generic Kaluza-Klein–like models and some particular cases of Beckenstein theory. Bounds on the free parameters of the different theories are obtained. Furthermore, we find that none of the proposed models is able to explain recent results (as from Webb and coworkers in 1999 and 2001) claiming an observed variation of the fine-structure constant from quasar absorption systems at redshifts 0:5 < z < 3.