This review is devoted to a systematic exposition of the basic ideas and consequences of duality and the Veneziano model for two-particle and multi-particle processes. It contains an attempt to give an answer to the question as to whether dual models can be regarded as a first approximation in describing the strong interactions. In this connection, emphasis is placed on the discussion of the qualitative consequences of the basic assumptions of duality and their detailed comparison with the experimental data. In addition, the review contains a discussion of the basic theoretical assumptions of duality, various specific variants of dual models and their application to experimentally observed reactions, as well as the difficulties that have been encountered in the consistent development of the idea of duality. On the whole, the review reflects the status of the subject as it existed in June 1971.