Because of their compact structure, ease of processing and higher heat transfer coefficient, curved-tube heat exchangers are widely applied in various industry applications, such as nuclear power systems, solar-powered engineering, aircraft engine cooling systems and refrigeration and cryogenic systems. Accurate knowledge about the heat transfer characteristics of the supercritical fluids in the tube is critical to the design and optimization of a curved-tube heat exchanger. The available literature indicates that the flow of supercritical fluids flowing in curved tubes affected by the dual effects of the buoyancy force and centrifugal force is more complex compared to straight tubes. Therefore, to obtain insight into their unique characteristics and further research progress, this paper presents a comprehensive review of available experimental and numerical research works on fluids at supercritical pressure flowing in curved tubes. Overall, the secondary flow caused by the curvature enhances the heat transfer and delays the heat transfer deterioration, but it also causes a non-uniform heat transfer distribution along the circumferential direction, and the strengthening performance of the curved tube is damaged. Compared with the more mature theories regarding straight tubes, the flow structure, the coupling mechanism of buoyancy and centrifugal force, and the general heat transfer correlation of supercritical fluids in a curved tube still urgently need to be further studied. Most importantly, studies on the suppression of heat transfer oscillations and heat transfer inhomogeneities specific to curved tubes are scarce. Considering the current status and shortcomings of existing studies, some study topics for supercritical fluids in a curved tube are proposed