With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings, discussing the importance of the basis selection, predictions from a SM effective field theory, and possible ways to measure these couplings with special attention to the high-energy regime. Predictions from the MSSM and MCHM, with the comparison with data, are also provided.

19 pages, contribution to the 2014 European School of High-Energy Physics