The framework of Effective Field Theory (EFT) Lagrangians is an effective and systematic way to search for physics beyond the Standard Model at the LHC using distributions of events in many topologies. A large number of measurements performed by ATLAS and CMS experiments in the Higgs sector of the Standard Model include EFT interpretations. They provide complementary constraints, although with various choices of bases and interpretation frameworks. No significant deviations from the Standard Model predictions have been observed so far, as constraints on relevant Wilson coefficients have been extracted.