The Higgs sector of the MSSM has a richer structure with respect to the SM, with characteristic phenomenological signatures both at high- and at low-energies.

After a brief overview of this sector and its phenomenological signatures, we present the results of a recent global fit of the MSSM in its constrained version (MSUGRA).

Within this minimal framework indirect constraints from flavour physics, electroweak observables, and dark matter, can easily be satisfied, and the lightest Higgs boson mass is predicted to be just above the LEP exclusion bound.