The application of latent thermal energy storage with heat pumps has been extensively studied in recent years. The combination of phase change heat storage and a heat pump can improve the performance of the heat pump and the utilization of renewable energy; however, further cost reduction and efficiency increase are required. Therefore, this study reviews the progress of heat pumps coupled with solid-liquid phase change materials and summarizes the applicable conditions and characterization methods for phase change materials applied to heat pumps. The optimization approaches for the performance of the heat pump system are summarized, including the selection and improvement of phase change materials, the optimal setting of the heat exchanger, and the dynamic optimization control strategy of the system. The outstanding performance of heat pumps with cascade heat storage in improving the supply-side comfort and utilization rate of renewable energy indicates the broad prospect of cascade heat storage being applied to heat pump energy storage systems. Herein, mixed, non-eutectic phase change materials are proposed as alternative materials for cascade heat storage. Notably, summarizing and developing new methods for adjusting the thermophysical properties of phase change materials for energy storage is necessary for adapting the selection and improvement of phase change materials to the optimization of the thermodynamic cycle of cascade heat storage devices and further improving the heating decarbonization ability of latent heat storage heat pumps.