While the Higgs and top quark phenomenology programmes are well underway, direct signs for new physics beyond the Standard Model remain elusive. In this talk, I will discuss the implications of recent LHC Higgs measurements from an Effective Field Theory (EFT) perspective. In particular, I will highlight the importance of differential distributions to obtain stringent constraints on new physics in the Higgs and top quark sectors sector and how theoretical uncertainties can limit the sensitivity of such an approach in the future. The latter is illustrated with a concrete physics scenario that extends the EFT description with new light degrees of freedom
