Beyond the Standard Model Higgs searches at the LHC

The Run I at the LHC marks the birth of the "Higgs physics", a path which will be followed at its full extent in the future runs of the LHC. Indeed there are two complementary paths to be followed to new physics in the Higgs sector: precision measurements of the Higgs properties (couplings, mass, spin and parity), where new physics can manifest as deviation from the Standard Model, or direct search for processes not foreseen in the Standard Model (Higgs decays not foreseen in the Standard Model, additional scalars which would indicate an extended Higgs sector). The current status of these studies at the LHC is presented, focussing in particular on the direct searches for rare or invisible Higgs decays or for an extended Higgs sector. The results are based on the analysis of the proton-proton collisions at 7 and 8 TeV center-of-mass energy at the LHC by the ATLAS and CMS collaborations.