Quark-Hadron Duality: the 't Hooft Model and Beyond

I review the notion of the quark-hadron duality from the modern perspective. Both, the theoretical foundation and practical applications are discussed. The proper theoretical framework in which the problem can be formulated and treated is Wilson's operator product expansion (OPE). Two models developed for the description of duality violations are considered in some detail: one is instanton-based, another resonance-based. The mechanisms they represent are complementary. Although both models are rather primitive (their largest virtue is their simplicity) they hopefully capture important features of the phenomenon. Being open for improvements, they can be used "as is" for orientation in the studies of duality violations in the processes of practical interest.