Simplified template cross-sections provide a detailed description of the properties of Higgs boson production at the LHC. These properties are most precisely determined in the combination of the measurements performed in the different Higgs boson decay channels. This article presents these combined measurements, as well as their interpretations in the context of specific scenarios of physics beyond the Standard Model, as well as in generic extensions within the framework of the Standard Model Effective Field Theory. A combination of measurements of the branching fractions of Higgs boson decays into invisible particles is also presented, and interpreted as constraints on the cross-section of WIMP dark matter interactions with nucleons. Through the combination between the analyses from ATLAS and CMS experiments, the evidence of the Higgs decay into a Z boson and a photon is established.