  We review the constraints on Higgs boson properties from effective potential
methods. In the Standard Model, the requirement of stability (or metastability)
of the standard electroweak minimum puts an upper bound on the scale of new
physics as a function of the Higgs mass. This upper bound is below the Planck
scale if the Higgs weights $\simlt$ 130 GeV. In supersymmetric extensions of
the Standard Model the former methods are useful to compute the Higgs mass
spectrum, and couplings, after resumming higher loop effects. In particular, if
the Higgs mass weights $\simgt$ 130 GeV, the minimal supersymmetric extension
of the Standard Model will be ruled out, while its non-minimal supersymmetric
extension containing singlets is only marginally allowed.
