Compact and rapid heat transfer technology can, within ultra-confined spaces and on the order of milliseconds, efficiently capture and transport large amounts of heat from the intake or internal components. It is the core determinant of both performance and technical success for a precooled engine. Conventional civil use heat exchanger analysis, design procedures, and experimental testing approaches are insufficient for validation due to the harsh operating environment and demanding performance requirements inside such systems. Therefore, conducting highly targeted, application oriented research on compact and rapid heat transfer technology specifically for precooled engines carries significant academic and engineering value. In this paper, the research progress of compact and rapid heat transfer technology from multiple dimensions, including underlying mechanisms, technical approaches, and experimental methods, is systematically reviewed, and the principal challenges it faces when applied to precooled engines are analyzed. Existing studies have yielded extensive and in-depth results in several areas: the mechanisms of rapid and intensive heat transfer of supercritical working fluids in microscale channels and cross-flow tube bundles; rapid simulation and similarity analysis methods for fluids with sharply varying properties; refined and uncertainty quantification based design methodologies; and experimental testing techniques tailored for extreme thermal environments in confined spaces, etc. Overall, in terms of fundamental research, it is urgent to deepen our understanding of the coupled flow heat transfer mechanisms under complex thermal conditions at micro scales and to further enrich high accuracy empirical correlation databases for compact and rapid heat transfer. From an analysis and design perspective, attention should be paid to integrating emerging techniques into analysis and design methods to enhance overall performance across broad operating ranges. In terms of experimental validation, more sophisticated flow-field measurement techniques appropriate for intricate structures in confined spaces must be developed, and complete temperature and full pressure testing must be conducted under actual engine installation circumstances. These research efforts will provide a solid foundation for improving the maturity of compact and rapid heat transfer technology and for advancing and validating precooled engine technology.