  The Fermi effective theory of the weak interaction helped identify the
structure of the electroweak sector of the Standard Model, and the chiral
effective Lagrangian pointed towards QCD as the theory of the strong
interactions. The Standard Model Effective Field Theory (SMEFT) is a systematic
and model-independent framework for characterizing experimental deviations from
the predictions of the Standard Model and pointing towards the structures of
its possible extensions that is complementary to direct searches for new
physics beyond the Standard Model. This talk summarizes results from the first
global fit to data from LHC Run 2 and earlier experiments including dimension-6
SMEFT operators, and gives examples how it can be used to constrain scenarios
for new physics beyond the Standard Model. In addition, some windows for
probing dimension-8 SMEFT operators are also mentioned.
