Many extensions beyond the Standard Model (BSM) predict new interactions between quarks and leptons above the electroweak scale. At lower energies, these interactions can be described by effective four-fermion operators that modify the semi-leptonic decays of mesons and baryons. Crossing symmetry ensures that these interactions will also leave an imprint in the 2->2 scattering of quarks into leptons at high-energy hadron colliders. In this talk, we focus on this last case and use the latest run-II LHC measurements in the high-pT "Drell-Yan tails" from dilepton (pp→ll) and monolepton (pp→lv) production to set limits on non-resonant New Physics models. We give results for various tree-level models with arbitrary flavor structures, these include d=6 SMEFT operators and leptoquarks. To this purpose, we introduce a new Mathematica package called "HighPT" that allows users to easily build complete LHC likelihoods for these New Physics scenarios enabling them to derive robust constraints on BSM parameter space. Furthermore, we also comment on the SMEFT truncation, the impact of d=8 operators, the effects of different CKM alignments and the complementarity between high-pT and low-energy flavor probes.