The microstructure development during a cooling period of alloys being immiscible in the liquid state such as AlPb or Al-Bi has gained renewed scientific and technical interest during the last decades. Experiments have been performed to investigate the phase transformation kinetics in the liquid miscibility gap and numerical models have been developed to simulate and analyze the solidification process. The recently developed computational modeling techniques can, to some extent, be applied to describe the decomposition, the spatial phase separation and the microstructure evolution during a cooling period of an immiscible alloy through the miscibility gap. This article overviews the researches in this field.