  Run I of the LHC has not revealed any sign of new physics beyond the Standard
Model (BSM). However, the discovery of an SM-like Higgs boson with mass around
125 GeV opens up new possibilities for probing various BSM scenarios with
enlarged Higgs sectors and/or new particles affecting the loop-induced
processes or opening new decay modes. We will present how we derive constraints
on new physics from the Higgs measurements performed by the ATLAS and CMS
collaborations. The impact of these measurements will then be assessed in the
context of the general phenomenological Minimal Supersymmetric Standard Model
(MSSM) and in the MSSM with a light neutralino as a dark matter candidate.
