In the context of carbon peaking as well as carbon neutral, energy storage, as well as energy saving technology, have become a research hot spot. The combination of energy-saving heat pump (HP) and phase change material (PCM) with high heat storage density can greatly improve the performance of HP. Therefore, HP coupled with PCM has received wide attention. In this paper, firstly, we overview the classification, thermophysical properties and modification of PCM for HP system. Then thermal energy storage (TES) for thermal energy supply and defrosting on both sides of condenser and evaporator are summarized in detail. Furthermore, the frontier technologies of coupling HP with PCM driven by renewable energy are introduced. Finally, the existing prob-lems, solutions, and future research directions are put forward.