Constraints on New Physics from the Higgs and Top Masses

Triviality and vacuum stability bounds on the Higgs and top quark masses in a rather general class of supersymmetric extensions of the Standard Model are compared with the corresponding bounds without supersymmetry. Due to generic differences of those bounds we find that experimental knowledge of the Higgs and top masses may provide a ``pointer'' into one of these directions. Depending on the values of the masses, however, both scenarios or none could also be allowed.