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We use top quark pair production as a probe of top-philic non-resonant new physics. Following a low energy effective field theory approach, we calculate several key observables in top quark pair production at hadron colliders (e.g., total cross section, tt invariant mass distribution, forward-backward asymmetry, spin correlations) including the interference of the Standard Model with dimension-six operators. We determine the LHC reach in probing new physics after having taken into account the Tevatron constraints. In particular, we show that the gluon fusion process gg → tt which remains largely unconstrained at the Tevatron is affected by only one top-philic dimension-six operator, the chromo-magnetic moment of the top quark. This operator can be further constrained by the LHC data as soon as a precision of about 20% is reached for the total tt cross-section. While our approach is general and model-independent, it is particularly relevant to models of Higgs and top compositeness, which we consider in detail, also in connection with tttt and ttbb production.