Considerable deviations from equilibrium conditions are observed for nonstatic, first-order phase transitions. In some cases, unstable (labile) phase states may precede the onset of the phase transition. The relaxation of the system is then accompanied by an enhancement of random inhomogeneities and the appearance of a modulated intermediate structure. This mechanism of the initial stage of a phase transition is called spinodal decomposition (SD). Theoretical and experimental studies of SD in two-component systems are reviewed in this paper. Thermodynamic stability and the possibility of SD in one-component liquid-vapor systems and an alternative nucleation mechanism are discussed. The phenomenological theory of SD is based on the Ginzburg-Landau expression for the free energy of an inhomogeneous system. A linearized diffusion equation is derived, for which thermodynamically unstable states have exponentially increasing solutions for the Fourier components of composition. Subsequent refinements of SD theory take into account thermal fluctuations and involve the derivation of the kinetic equation for the distribution functional. Diffraction methods are the most effective in the experimental study of SD in alloys, glasses, and binary liquid mixtures. So far, the agreement between theory and experiment must be regarded as only qualitative.