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The Large Hadron Collider can do precision physics at a level that is competitive with elec-troweak precision constraints when probing physics beyond the Standard Model. We present a simple yet general parameterization of the effect of an arbitrary number of lepton-quark contact interactions on any di-lepton observable at hadron colliders. This parameterization can be easily adopted by the experimental collaborations to put bounds on arbitrary combinations of lepton-quark contact interactions. We compute the corresponding bounds from current di-lepton resonance searches at the LHC and find that they are competitive with and often complementary to indirect constraints from electroweak precision data. We combine all current constraints in a global analy-sis to obtain the most stringent bounds on lepton-quark contact interactions. We also show that the high-energy phase of the LHC has a unique potential in terms of discovery and discrimination power among different types of lepton-quark contact interactions. The Large Hadron Collider (LHC) is a discovery machine at the energy frontier. However, it can also do precision physics, probing physics beyond the Standard Model (SM) in a complementary and even competitive way to electroweak precision data (EWPD). Model-independent bounds on departures from the SM can be systematically computed by means of effective Lagrangians. Assuming the SM particle content and symmetries and neglecting lepton number violation, the leading corrections arise from dimension-six operator