Abstract
Nowadays, the Standard Model Effective Field Theory (SMEFT) provides a standard framework to parameterize potential deviations from the Standard Model and to combine information from multiple processes in global analyses. This review summarizes dedicated studies that constrain dimension-six Wilson coefficients using three top-quark and four top-quark production processes. We highlight the complementarity of these channels, as well as summarize the main problems and prospects in the area. A concise introduction to the SMEFT formalism and a discussion of the problem of potential perturbative unitarity violation are also provided.
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