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[Display omitted] • The hysteresis is due to the difference of primary nucleation mechanism during heating and cooling. • The PCH is related to the properties of the material itself and the experimental measurement conditions. • The hysteresis temperature is positively correlated with the heating/cooling rate. • The hysteresis effect is more obvious in an incomplete phase transition. • Numerical models of the hysteresis effect of complete and incomplete phase transition are summarized. As an efficient energy storage material, phase change material can be combined with lightweight buildings to reduce the energy consumption of the building envelopes effectively, while it is often accompanied by phase change hysteresis(PCH) and supercoiling (SC) phenomena during the phase transition. SC means that the nucleation does not solidify at the theoretical solidification temperature and needs to be nucleated at a lower temperature. PCH indicates the difference between the melting temperature and the solidification temperature of the phase change materials (PCMs). So far, a lot of research on SC has been done and there is still a lack of research on PCH. On the one hand, the PCH is proportional to the energy loss of the system, the latent heat of PCMs cannot be exploited if PCH is beyond the operating temperature range of the system. On the other hand, when PCMs are combined with building envelopes, the greater the hysteresis temperature, the better the thermal performance of the wall. It's vital to use the hysteresis temperature to improve the performance of the system. Especially, PCMs are equipped in building envelopes, the hysteresis phenomenon of incomplete phase transition will be more obvious because of large temperature fluctuation outside. The hysteresis effect of PCMs in building envelopes is discussed in this paper, the numerical simulation methods and experimental research of PCH are reviewed and analyzed from two aspects of complete and incomplete phase transition. It showed that the PCH should be considered when simulating the thermal behavior of PCMs in building envelopes. The results would be more accurate if two enthalpy-temperature curves (H(T) curve) are used to represent the melting and solidification process, respectively. In addition, the nucleation mechanism of PCH has not been discussed in previous articles and there is no explanation about whether the hysteresis phenomenon is caused by the properties of the material itself or is affected by experimental measurement conditions. Therefore, the related issues are discussed in this paper, it is considered that the PCH is not only related to the properties of the materials but also affected by the experimental measurement conditions. [ABSTRACT FROM AUTHOR]