Precision tests of the Standard Model (SM) based on electroweak precision observables have proven the quantum consistency of the SM gauge theory to extreme precision. With increasing precision being reached for a broader spectrum of collider and flavour-physics measurements, it is now possible to perform more global fits that also include Higgs-boson, top-quark, di-boson, Drell-Yan, and flavour-physics observables. This is particularly interesting to test those areas of the SM that still depend on a large number of relatively arbitrary parameters, such as the scalar potential, scalar-fermion interactions, and flavour dynamics. After a brief update on the status of electroweak precision fits of the SM, we will present results from a more general analysis of the Standard Model Effective Field Theory (SMEFT). The study uses the Bayesian-based open-source HEPfit fitting framework where SMEFT and SM parameters are simultaneously floated and fit. We limit our analysis to dimension-six SMEFT operators and calculate theoretical predictions for each observable at linear order in the corresponding Wilson coefficients. We study the role played by different kinds of observables in constraining the SMEFT interactions and setting a lower bound on the scale of new physics. To explore in particular the role played by flavour observables, we consider two possible scenarios in which the SMEFT coefficients inherit a U(3)^5 or U(2)^5 flavour symmetry from the parent UV theory.