Dark matter and neutrino masses provide up to now the only clear pieces of evidence of physics beyond the Standard Model. On the other hand, the LHC discovery of a new particle with a mass of 126 GeV, compatible with the properties of a Standard Model Higgs boson, puts severe constraints on new physics models. In this talk, we briefly review these implications and investigate them in some detail for the specific cases of general supersymmetric and minimal dark matter models. Particular attention is paid to coannihilation effects and radiative corrections.