Understanding the heat transfer limits of heat exchangers for aero-engines within the flight envelope and expanding their performance boundaries are critical measures to advance aero-engines toward higher thrust-to-weight ratios. This paper focuses on the design requirements of heat exchangers used in cooled cooling air technology. First, the structures of typical air heat exchangers in aero-engines and novel heat exchanger structures with promising applications are reviewed. Then, the method for analyzing and expanding the performance boundaries of heat exchangers within the flight envelope is proposed to ensure the stable and efficient operation of the aero-engines under complex working conditions. The performance boundary range of non-uniformly arranged serpentine tube heat exchangers is also provided. Subsequently, the existing heat exchanger performance evaluation methods are reviewed, and the comprehensive performance evaluation plot for aero-engine heat exchangers is developed. Finally, the development prospects of air heat exchangers for aero-engines are discussed.