It is suggested that a dual model could provide a Born approximation to a complete theory of hadrons. After reviewing various properties of Veneziano model amplitudes, including their underlying algebraic structure, more recent developments are discussed. The spectrum generating algebra is constructed and used to prove the no-ghost theorem for space-time dimension d < 26. A modification of the Veneziano model incorporating SU(A0 symmetry in a dynamical fashion is shown to have critical dimension 26 -N. A detailed discussion of the dual pion model and its extension to fermions is presented. It is proved that both the meson and fermion sectors are ghost free for d < 10. Finally, there is a discussion of nonplanar models and their possible connection with the pomeron singularities arising from nonplanar loop diagrams.