We analyze the implications of a Higgs discovery on possible ``new-physics''
scenarios, for mH up to ∼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.Comment: 12 pages, LaTeX file, 3 figures, full postscript version also
available at http://hpteor.lnf.infn.it/papers.htm