<p>In industrial manufacturing, nuclear engineering, aerospace and other related fields, the heat flux density applied to relevant equipment has been continuously increasing. To address this problem, jet heat transfer technology is widely used due to its advantages of low pumping pressure and high heat transfer rate. Based on different operating conditions, the jet impingement surfaces are mainly classified into concave/convex structures; the core justifications for this classification in this paper are as follows: concave and convex surfaces are the most typical and widely used types of curved jet impingement surfaces in practical engineering, and their heat transfer characteristics have the strongest correlation with operating conditions (such as jet velocity, heat flux, nozzle distance, etc.), which can intuitively reflect the intrinsic correlation law of "operating conditions—impingement surface structure—heat transfer performance", consistent with the core research theme of "curved surface jet enhanced heat transfer" in this paper. In this paper, the enhanced heat transfer schemes applicable to these two curved structures in recent decades are summarized and discussed respectively. Firstly, the effect of the number of jet nozzles, their arrangement, and nozzle geometry on the jet heat transfer rate is discussed. Secondly, the effect of flow regimes (e.g., swirling, pulsating, and sweeping jets), coolant type, and jet impingement surface structure on heat transfer performance is discussed; meanwhile, the influence of other key parameters such as inlet velocity profile, jet inclination, target surface conditions, confinement, and nozzle-to-target distance on heat transfer is also considered. Finally, the heat transfer predictive models for concave/convex jet impingement surfaces, the turbulence equations selected for numerical simulations, and the related devices for flow and heat transfer visualization in experimental studies are summarized and analyzed, with suggestions for future work provided.</p>