Abstract: Before the advent of duality (late 60s) two disconnected phenomena were studied in the dynamics of strong interactions: low-energy resonances and high-energy smooth asymptotic behavior. With the discovery of duality and its realization by the Veneziano model that unified the low- and high-energy regions the situation changed drastically. Various versions of dual models and their practical applications were proposed and applied to describe physical reactions. An important virtue of dual models is the possibility of their multiparticle generalizations. Duality also stimulated the birth of new ideas, including supersymmetry.
On the other hand, progress in further development and practical applications of dual models was limited by problems with unitarity, partially resolved by a group of theorists at the Bogolubov Institute for Theoretical Physics (Kiev, Ukraine), in the so-called Dual Amplitude with Mandelstam Analyticity (DAMA) by use of non-linear, complex Regge trajectories. A further development was related to off-mass-shell modifications of DAMA, known as MDAMA (V. Magas et al.). Recently we are witnessing a revival of the ideas of duality, partly in formal mathematical constructions such as q-deformed dual amplitude.
The basic idea and goal remain topical and timely: understanding and unified description of various elastic and inelastic reactions in a wide range of kinematical variables.