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Since the discovery of the Higgs boson in 2012 by the ATLAS and CMS Collaborations a lot of progress has been made in verifying the nature of this new bosonic particle. Still, questions remain as to whether this new particle is the standard model (SM) Higgs boson, and whether it gives us hints of where physics beyond the SM (BSM) might be hidden. This overview tries to tackle these questions by looking at three types of analyses 1) Total cross section measurements of the various Higgs boson production and decay modes, allowing us access to the various Higgs boson couplings to SM bosons and fermions, 2) Differential Higgs boson cross section measurements such as in the STXS framework allowing for a model independent search for BSM and, finally, 3) The searches for di-Higgs production which give access to the trilinear Higgs self coupling and the Higgs potential itself.
T. Lange (Mon,) studied this question.