Anatomy of the Higgs mass spectrum

We analyze the implications of a Higgs discovery on possible ``new-physics'' scenarios, for $m_H$ up to $\sim 700$ GeV. For this purpose we critically review lower and upper limits on the Higgs mass in the SM and in the MSSM, respectively. Furthermore, we discuss the general features of possible ``heavy'' ($m_H \gsim 2 m_Z$) Higgs scenarios by means of a simple heavy-fermion condensate model.