Latent heat thermal energy storage (LHTES) has recently attracted increasing interest related to the thermal applications, and has been studied by researchers using theoretical and numerical approaches. The heat transfer mechanisms during the charging and discharging periods of the phase change materials (PCMs) and two basic problems for phase transformations have been discussed in this paper. 1D, 2D and 3D popular mathematical solutions based on the heat transfer mechanisms of conduction and/or convection have been analyzed. Then, various numerical models for encapsulated PCMs in terms of macro-encapsulated PCM and micro-encapsulated PCM were investigated. The numerical simulation of heat transfer problems in phase change processes is complicated and the achieved results are approximate according to a number of conditions. The accuracy of numerical solution depends on the assumptions that are made by the authors. Therefore this review will enable the researchers to have an overall view of the mathematical and numerical methods used for PCM׳s phase transformations. It offers the researcher a guideline of selecting the appropriate theoretical solutions according to their researches׳ purposes.