Operator Product Expansion and Quark-Hadron Duality: Facts and Riddles

We review the status of the practical operator product expansion (OPE), when applied to two-point correlators of QCD currents which interpolate to mesonic resonances, in view of the violations of local quark-hadron duality. Covered topics are: a mini-review of mesonic QCD sum rules in vacuum, at finite temperature, or at finite baryon density, a comparison of model calculations of current-current correlation functions in 2D and 4D with the OPE expression, a discussion of meson distribution amplitudes in the light of nonperturbatively nonlocal modifications of the OPE, and a reorganization of the OPE which (partially) resums powers of covariant derivatives.