This paper presents a comprehensive review of significant studies that are relevant to thermal energy storage technologies using phase change materials (PCMs). The review focuses on the techniques applied to enhance the performance of thermal storage systems and the methods used to analyse the heat transfer problems in PCMs. In addition, this paper reviews the published results and discussions on the heat transfer intensification methods including application of fins, filling materials, nano-fluids, nano-particles, microencapsulation and the thermal conductivity enhancement method. Furthermore, the experimental and mathematical methods to enhance the thermal conductivity of PCMs are summarised, and the methods used to determine the nanofluid dynamic viscosity in recent investigations are also listed and discussed. The focus of this review is to provide a solid basis for the identification of the optimal design for the various heat transfer applications using PCM.