  The search for the a Standard Model Higgs boson at the LHC is reaching a
critical stage as the possible mass range for the particle has become extremely
narrow and some signal at a mass of about 125 GeV is starting to emerge. We
study the implications of these LHC Higgs searches for Higgs portal models of
dark matter in a rather model independent way. Their impact on the cosmological
relic density and on the direct detection rates are studied in the context of
generic scalar, vector and fermionic thermal dark matter particles. Assuming a
sufficiently small invisible Higgs decay branching ratio, we find that current
data, in particular from the XENON experiment, essentially exclude fermionic
dark matter as well as light, i.e. with masses below 50 GeV, scalar and vector
dark matter particles. Possible observation of these particles at the planned
upgrade of the XENON experiment as well in collider searches is discussed.
