Effective interactions and new physics at the LHC

While the Higgs and top characterisation 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 measurements from an Effective Field Theory perspective. In particular, I will highlight the importance of differential distributions to obtain stringent constraints on new physics in the Higgs sector and how theoretical uncertainties can limit the sensitivity of such an approach in the future. Finally, I will comment on constraints on new degrees of freedom that can arise in UV complete composite Higgs theories.