  We present a global interpretation of Higgs, diboson, and top quark
production and decay measurements from the LHC in the framework of the Standard
Model Effective Field Theory (SMEFT) at dimension six. We constrain
simultaneously 36 independent directions in its parameter space, and compare
the outcome of the global analysis with that from individual and two-parameter
fits. Our results are obtained by means of state-of-the-art theoretical
calculations for the SM and the EFT cross-sections, and account for both linear
and quadratic corrections in the $1/\Lambda^2$ expansion. We demonstrate how
the inclusion of NLO QCD and $\mathcal{O}\left( \Lambda^{-4}\right)$ effects is
instrumental to accurately map the posterior distributions associated to the
fitted Wilson coefficients. We assess the interplay and complementarity between
the top quark, Higgs, and diboson measurements, deploy a variety of statistical
estimators to quantify the impact of each dataset in the parameter space, and
carry out fits in BSM-inspired scenarios such as the top-philic model. Our
results represent a stepping stone in the ongoing program of model-independent
searches at the LHC from precision measurements, and pave the way towards yet
more global SMEFT interpretations extended to other high-$p_T$ processes as
well as to low-energy observables.
