Energy storage components improve the energy efficiency of systems by reducing the mismatch between supply and demand. For this purpose, phase-change materials are particularly attractive since they provide a high-energy storage density at a constant temperature which corresponds to the phase transition temperature of the material. Nevertheless, the incorporation of phase-change materials (PCMs) in a particular application calls for an analysis that will enable the researcher to optimize performances of systems. Due to the non-linear nature of the problem, numerical analysis is generally required to obtain appropriate solutions for the thermal behavior of systems. Therefore, a large amount of research has been carried out on PCMs behavior predictions. The review will present models based on the first law and on the second law of thermodynamics. It shows selected results for several configurations, from numerous authors so as to enable one to start his/her research with an exhaustive overview of the subject. This overview stresses the need to match experimental investigations with recent numerical analyses since in recent years, models mostly rely on other models in their validation stages.