  The search for effective field theory deformations of the Standard Model (SM)
is a major goal of particle physics that can benefit from a global approach in
the framework of the Standard Model Effective Field Theory (SMEFT). For the
first time, we include LHC data on top production and differential
distributions together with Higgs production and decay rates and Simplified
Template Cross-Section (STXS) measurements in a global fit, as well as
precision electroweak and diboson measurements from LEP and the LHC, in a
global analysis with SMEFT operators of dimension 6 included linearly. We
present the constraints on the coefficients of these operators, both
individually and when marginalised, in flavour-universal and top-specific
scenarios, studying the interplay of these datasets and the correlations they
induce in the SMEFT. We then explore the constraints that our linear SMEFT
analysis imposes on specific ultra-violet completions of the Standard Model,
including those with single additional fields and low-mass stop squarks. We
also present a model-independent search for deformations of the SM that
contribute to between two and five SMEFT operator coefficients. In no case do
we find any significant evidence for physics beyond the SM. Our underlying
$\tt{Fitmaker}$ public code provides a framework for future generalisations of
our analysis, including a quadratic treatment of dimension-6 operators.
