Crystallization of amorphous alloys is compared with conventional solidification of melts. Taking account of the temperature dependence of crystal nucleation and growth rates, the links between the two processes are explored. The fundamentals of nucleation and growth kinetics in amorphous alloys are reviewed. It is shown that the crystallization of amorphous alloys can be exploited (1) to obtain ultrafine grained microstructures with useful properties and (2) to elucidate nucleation mechanisms in conventional grain-refining practice.