Prospects for physics at high luminosity with CMS

The precision measurements of the properties of the recently discovered Higgs-like boson will be central to the future LHC physics program. In parallel the search for New Physics beyond the SM will continue. Higher luminosity will extend the mass reach and allow sensitive searches for possible subtle signatures for new physics. In this paper we review the potential sensitivity of CMS to a selection of relevant future physics scenarios accessible with the LHC upgrades and a correspondingly upgraded CMS detector.