A review is given of the theory of strong interactions based on the model in which hadrons are represented as one-dimensional elastic relativistic systems (``strings''). The relation between this model and the concepts of quarks and partons is discussed. Basic results pertaining to Veneziano's dual theory, which can be regarded as a consequence of the string model, and modifications of this theory are considered. A detailed account of the classical theory of strings is given. The main emphasis is on those problems which are important in constructing a quantum theory, namely Hamiltonian mechanics and conformal symmetry. The quantization procedure is described and is shown to be self-consistent only in a 26-dimensional space with a special condition on the spectrum of states. A theory of strings with distributed spin is considered. Spin is introduced by means of the formalism of Grassman algebras. Quantization is then possible only in a 10-dimensional space. Interactions of strings take place by virtue of their rupture and recombination. A method of calculating interaction amplitudes is given. Discussions of the Koba-Nielsen representation, the continuum integral, and the two-dimensional conformal group are included in an appendix.