The Supersymmetric Higgs bounds at the Tevatron and the LHC

MSSM Higgs bosons are the most promising way to discover Higgs physics at hadronic colliders since their cross section is enhanced compared to that of the Standard Model. We will present theoretical predictions for their production and decay in the Higgs$\to \tau \tau$ channel at the Tevatron and the LHC, focusing on the theoretical uncertainties that affect them. The inferred SUSY Higgs bounds on the $[\tan \beta ; M_A]$ plane and the impact of these uncertainties will also be discussed.