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Spurred by the discovery of a boson resonance at the LHC as the result of thesearch for the Standard Model Higgs, we pursue our investigation of theproperties and signatures of Higgses in an effective supersymmetric scenariothat goes beyond the usual MSSM. Such scenarios were first introduced toalleviate the naturalness problem of the MSSM Higgs and are found to have avery rich phenomenology that allows departures from the Standard Model in theproduction rate of the Higgs in many of the search channels. We now include theconstraints from flavour observables in particular the rare decays b-> s gammaand Bs -> mu+ mu- including the recent measurement from LHCb. We also addressthe issue of Dark Matter and its impact on Higgs physics. In particular, weincorporate the latest data from XENON100 on the spin independent directdetection rates. These turn out to be powerful constraints, especially if onealso imposes that the observed thermal relic density is obtained. We also studymodels with a low abundance that can more easily evade the direct detectionrates. We study the impact of the flavour and Dark Matter observables on theproduction rates of the Higgs at the LHC, and their correlations in thediphoton, diphoton+jets and 4 leptons. We also comment on the other channels.

Supersymmetric Higgses beyond the MSSM: An update with flavour and Dark Matter constraints