A large number of systems based on III-V, II-VI, and IV-VI compounds exhibit complete solid miscibility or extensive composition ranges over which solid solutions can be formed. In these systems, the solid phase is a phase of variable composition with respect to two or more of the components; the composition variation allows one to obtain intermediate combinations of properties as compared with the properties of the initial compounds. The compound alloys find extensive applications in semiconductor devices that require a certain well-defined energy band structure, such as light or electron emitters, detectors, and heterojunction injection lasers. At present, most attention is centered on the III-V and IV-VI alloy systems that can be amphoterically doped and in which bandgaps extending from the far infrared to the visible green can be realized. In addition to these systems whose technology is presently well developed, a strong interest also exists in the II-VI compound solutions as well as in the (II-VJ)-(III-V) and (II-VI)-(IV-VJ) mixtures, mainly in view of the potential such alloys may hold for extending the bandgap region over which these II-VI compound-based systems can be amphoterically doped. The major difficulty in the growth of homogeneous alloy crystals from dilute or stoichiometric melts results from the differences in the equilibrium compositions of the liquid and solid phases, which leads to segregation during solidification and compositional variations in the grown crystals. A knowledge of the phase relationships that govern the growth of such alloys from solution is therefore essential. This paper discusses recent work concerning both the thermodynamic properties of solid solution alloys and the liquid-solid phase equilibrium conditions for growth of these alloys from ternary or quaternary solutions. No attempt is made to