Abstract: Whether the actual stall margin of the compressor can reach the design target directly determines whether the engine can be put into service. The current system of compressor aerodynamic design lacks an efficient and accurate tool to evaluate the stall margin, which maybe lead to great risk. Therefore, it is urgent to develop a fast and reliable compressor stability prediction tool for use in the design phase. The aerodynamic design of modern aircraft compressors is increasingly oriented towards three-dimensional refinement, and considering the effect of three-dimensional blade shapes on stability during the design phase has become crucial. Traditional excited disk and semi-excited disk models struggle to capture the intricate effects of three-dimensional blade shapes on flow stability, while unsteady numerical simulation methods demand too much computational resource during the compressor design phase. In order to simultaneously enhance the consideration of blade shape effects and improve computational efficiency, providing a stability assessment tool for the aerodynamic design phase, our team initially proposed a general theory for the flow stability of turbomachinery in 2013. This theory incorporates the impact of complex blade shapes through the modeling of distributed blade force sources, and the flow stability is described by system eigenvalues. Subsequently, three simplified models were developed to cater to different prediction objectives and application conditions: the meridional plane model, streamline model, and radial expansion model. Among these, the meridional plane model can accurately characterize the influence of critical design parameters such as blade tip clearance, blade sweep, and blade loading on flow stability, and can offer a reliable tool for predicting instability boundaries during the design phase. The streamline model can rapidly assess the flow stability of various streamline systems in the spanwise direction, and provide quantitative information on the regions of greatest flow instability to guide blade design for stability enhancement. The radial expansion model can rapidly predict the flow instability point of a centrifugal compressor, allowing for a quantitative evaluation of its flow stability. These models find application within the aerodynamic design framework of compressors, furnishing a dependable stability assessment method for finalized compressor designs. Consequently, they constitute a technological foundation for the integration of aerodynamics and stability in compressor design.