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• Recent advances in supercritical carbon dioxide power system are summarized. • The general and unique problems in coupling of supercritical carbon dioxide power cycle and different heat sources are identified. • The multiscale features of supercritical carbon dioxide power system are demonstrated. • Applications of supercritical carbon dioxide power system in nuclear, solar energy and fossil fuel are discussed. • An outlook on technical challenges is presented to promote industrial applications. Under the background of carbon reduction, the development of efficient power conversion system has drawn more important attention. The advantages of high efficiency and compactness have triggered increasing industrial interests in the applications of supercritical carbon dioxide power system for broad heat sources. However, when the supercritical carbon dioxide power cycle is coupled with different heat sources, there exist both general problems mainly associated with the supercritical carbon dioxide cycles and unique problems due to the heating processes of supercritical carbon dioxide. Moreover, the multiscale features of the supercritical carbon dioxide power system lead to significant challenges to theoretical analysis and engineering design. This review work provides the recent advances of supercritical carbon dioxide power systems, especially for the applications in heat sources of nuclear, solar and fossil fuel. With a focus on the category of general problems and unique problems, the current studies concerning the coupling of supercritical carbon dioxide power cycle with a specific heat source are further divided into three scales of system, component and process. The designs of the reactor core in nuclear, the receiver in concentrated solar power plant and the boiler in coal-fired power plant are discussed in detail at the scales of system, component and process. Future research directions for supercritical carbon dioxide power system are identified at different scales and more accurate integrated modelling for the coupling of supercritical carbon dioxide power cycle with specific heat sources are encouraged. The present work will benefit the in-depth understanding and further promotion of supercritical carbon dioxide power systems in industrial applications. [ABSTRACT FROM AUTHOR]