We have studied mixing of metal overlayers (Ni, Cr, Ti, W, Ta, Zr, Cu) on insulators (SiC, Si3N4, Al2O3, SiO2) after ion beam irradiation, rapid thermal annealing, and pulsed laser irradiation. The nature and amount of mixing varies from stoichiometric to continuous, to ballistic, to no mixing at all. For a given system, the amount of mixing was found to increase with increasing substrate temperature. The enhanced mixing with increasing substrate temperature is correlated with concomitant free energy associated with the reactions. Certain systems such as Cu on Al2O3 do not exhibit mixing, but rearrangement within a few atomic layers at the interface results in enhanced adhesion and no aggregation upon annealing at moderate temperatures.