As a core component of aero-engines, the continuous advancement of compressor aerodynamic design methods has long been a key driver for performance improvement. This paper reviews the technological evolution of these design methods over the past eight decades, systematically outlines the key characteristics of aerodynamic design development, and highlights the co-evolutionary relationship among innovations in design methodologies, breakthroughs in engine performance, and iterative advancements in computational technologies. Against the backdrop of exponential growth in computing power and algorithm efficiency, new compressor aerodynamic design approaches are emerging rapidly, accelerating the transition toward intelligent screening and multi-disciplinary coupling. Meanwhile, traditional low-dimensional empirical methods are being enhanced through intelligent algorithms that build general model libraries, enabling rapid evaluations within defined parameter ranges. In the context of the digital transformation of the aero-engine industry, the future compressor aerodynamic design system is expected to follow an integrated development path where empirical models, numerical simulations, and intelligent algorithms complement each other, achieving a co-evolutionary paradigm that combines innovative fusion with improved engineering efficiency.