In this paper we consider the degree of usefulness of the phase diagram and the related thermodynamics in predicting and understanding the formation of metastable phases during quenching, or during low-temperature solid-state interdiffusion, or during co-deposition. Recent research has demonstrated that many of such metastable phases are formed because the more stable intermediate phases that are favored thermodynamically are nevertheless bypassed kinetically. The kinetic elimination of intermediate phases provides conditions where a metastable equilibrium can be established at low temperatures between the supercooled liquid and the terminal solid solutions, leading to metastable partitioned two-phase regions. Alternatively, the range of the metastable phases may be governed by the T/sub 0/ principle related to the crossover of the respective free energy curves, or may be controlled mainly by kinetic considerations. Which particular thermodynamic conditions apply appears to depend on the initial form of the phase diagram and the specific technique used. The occurrence of massive transformations also is discussed. 34 refs., 10 figs.