In this talk I will discuss global fits of the Standard Model and models of new physics, illustrating how they have been extended to include a broad spectrum of collider observables beyond just precision electroweak observables. In the absence of direct evidence of new physics up to the scales so far explored by the Large Hadron Colliders (LHC), global fits become crucial to test the consistency of the Standard Model and point to anomalies that could be induced by the indirect effects of new physics well above the electroweak scale. Deciphering the origin of potential tensions with Standard Model predictions will require introducing new physics effects. The framework of effective field theories lends itself nicely to problems that, as in this case, involve a broad range of scales. In this talk I will consider the case in which new physics effects are described in the framework of the so called Standard Model Effective Field Theory (SMEFT) and show examples of how current global fits can constrain it.