With the discovery of the Higgs and precise measurement of its mass, all the parameters of the Standard Model (SM) are determined at the percent level. Measurements of the Higgs couplings are therefore searches for physics beyond the SM. Given a deviation from the SM, a model-independent bound on the scale of new physics can be obtained without theoretical assumptions using the fact that the theory violates tree-level unitarity in the absence of additional states. In this way, any measured deviation from the SM points to a new scale that can be a target for future experiments. This talk will present results for the scale of new physics and other model-independent implications of measurements of hhh, hVV, and htt couplings. For example, HL-LHC measurements consistent with current experimental limits may point to a scale of new physics below several TeV.