Understanding the phase transition processes in chalcogenide materials is of key importance for the development, optimization, and further scaling of phase-change memories (PCM). In particular, the transition from the amorphous to crystalline phase plays a crucial role in both programming and retention. Depending on the chosen material, either nucleation or growth processes are dominating this crystallization. In the first part of this article, different theoretical models for nucleation and growth are compared, and this for two typical phase-change materials. The second part of the article shows how finite element simulations can provide the direct link between these crystallization theories and operation and retention characteristics of a real PCM cell.