The measurements of the properties of the recently discovered Higgs boson show good agreement with the predictions from the Standard Model. The currently large uncertainties on the Higgs couplings will be improved in the high-energy and high-luminosity phase of the LHC as well as at a future Higgs factory, so that small deviations in the Higgs couplings may manifest themselves. In this talk typical new physics scenarios shall be reviewed that lead to observable modifications of the Higgs interactions. The coupling deviations in the various models will be related to their effective new physics scale, revealing that with percent level precision the Higgs coupings will be sensitive to the multi-TeV regime.