I will present two recent works related to the applications of the Standard Model Effective Field Theory (SMEFT). In the first work we present a global analysis of the LHC top-quark measurements. A novel framework called SMEFiT is developed, based on the Monte Carlo replica method, to derive global bounds for the 34 degrees of freedom relevant for the interpretation of the LHC top quark data. State-of-the-art theoretical calculations are adopted both for the Standard Model and for the SMEFT contributions. The second work focuses on weak vector boson scattering (VBS) processes, which probe new physics effects in the electroweak sector. While experimental constraints at the LHC are interpreted with dimension-8 SMEFT operators, we point out that by using fundamental principles of the UV completion, such as unitarity and analyticity, a set of “positivity bounds” on the dimension-8 coefficients can be derived. These bounds imply that the current SMEFT approach to VBS has a large redundancy: only ∼2% of the full parameter space may correspond to realistic UV completions. By excluding the unphysical region of the SMEFT parameter space, these bounds provide guidance for future VBS measurements at the LHC.