We have performed an updated global fit to precision electroweak data, W+W? measurements at LEP, and Higgs and diboson data from Runs 1 and 2 of the LHC in the framework of the Standard Model Effective Field Theory (SMEFT) (together with C. Murphy, V. Sanz and T. You). We exhibit the improvement in the constraints on dimension-6 operator coefficients provided by the LHC Run 2 data, and discuss the correlations between them. We also explore the constraints our fit results impose on several models of physics beyond the Standard Model, including models that contribute to the operator coefficients at the tree level and stops in the MSSM that contribute via loops. Finally, I mention pioneering limits on dimension-8 operators obtained from LHC data on isolated photon pairs (together with Shao-Feng Ge).
