Searches for new interactions within the SMEFT framework at present and future colliders

The existence of Beyond Standard Model (BSM) physics is firmly suggested by both experimental observations (Dark Matter, neutrino masses) and theoretical arguments. In the hypothesis that the scale of new physics is considerably higher than the energies probed at colliders, we can parametrise modified interactions induced by BSM effects among SM particles in a model-independent framework, the Standard Model Effective Field Theory (SMEFT). Searches for indirect evidence of new physics are conceptually different from the direct ones that have characterised the first part of the LHC program, and both experimental and phenomenological studies are needed in order to maximise the chances of uncovering a BSM signal. In this thesis, several phenomenological aspects of the SMEFT are discussed, both at present and future colliders. A characteristic feature of modified interactions is that they can induce unitarity violating effects which can be exploited to gain sensitivity. In this direction, a thorough study of the top quark electroweak sector will be presented, focusing on 2 to 2 scatterings and their embeddings in physical processes at colliders. This analysis allows us to identify several final states that have a good potential to explore the SMEFT parameter space and that could be particularly relevant in a global analysis. One of the key features of the SMEFT is indeed that deviations from the SM interactions are correlated and global interpretations are therefore of fundamental importance. A combined interpretation of the Higgs, top and diboson data from the LHC is here presented and the interplay between the various datasets discussed. Finally, the physics potential of a futuristic muon collider will be analysed, focusing in particular on the prospects to determine the Higgs self-interactions, a task that is arduous even in proposed 100 TeV proton colliders.