Theoretical implications of the possible observation of Higgs bosons at LEP

Theoretical implications of the possible observation of a Higgs boson with a mass of about 115 GeV at LEP are discussed. Within the Standard Model a Higgs boson in this mass range agrees well with the indirect constraints from electroweak precision data. However, it would nevertheless point towards physics beyond the Standard Model, in particular to Supersymmetric extensions. The interpretation of the LEP excess as production of the light or the heavy CP-even Higgs boson is discussed within the unconstrained MSSM and the mSUGRA, GMSB and AMSB scenarios. Prospects for Higgs physics at future colliders are briefly summarized.