  The LHC is already putting bounds on the Higgs mass. In this paper we use
those bounds to put constrains on the MSSM parameter space coming from the fact
that, in supersymmetry, the Higgs mass is a function of the masses of
sparticles, and therefore an upper bound on the Higgs mass translates into an
upper bound for the masses for superparners. We show that, although current
bounds do not constrain yet the MSSM parameter space from above, once the Higgs
mass bound improves big regions of this parameter space will be excluded,
putting upper bounds on SUSY masses. On the other hand, for the case of
split-SUSY we will show that, for moderate or large tan\beta, the present
bounds on the Higgs mass already imply that the common mass for scalars cannot
be greater than 10^{11} GeV. We show how these bounds will evolve as long LHC
improves the limits on the Higgs mass.
