The basic principles of a family of crystal-growing techniques in which crystallisation of a substance is achieved via diffusion through a thin alloy zone (TAZ) from a third phase (solid, liquid, or vapour) are described. Crystallisation is achieved by the application of a gradient of a thermodynamic potential across the zone and various methods of establishing such a gradient are considered. A theory predicting the velocity of a TAZ along a solid charge, published previously (D. T. J. Hurle, J. B. Mullin, and E. R. Pike, Phil. Mag. 9 (1964) 423), is extended to include the case where one of the solid phases is metastable. Expressions for the gradient of constitutional supercooling in the zone are derived for conventional and thin alloy zone crystallisation (TAZC) processes. It is shown that the important advantage in the use of a TAZ is the dramatic reduction in the supercooling at a given velocity compared to conventional processes. A rationalisation of various published techniques of crystal growth within the concepts of TAZC is presented and some existing and potential applications of TAZC processes are reviewed.