Abstract: Global linear stability analysis serves as a fundamental methodology for investigating flow instability mechanisms, with extensive applications in problems such as flow past bluff bodies. This approach transforms the linearized initial-value problem governing the temporal evolution of infinitesimal perturbations superimposed on steady base flows into an eigenvalue problem. The solution yields direct modes along with their corresponding frequencies and growth rates, enabling the assessment of flow instability under given base flow conditions. While capable of characterizing the exponential growth or decay of small-amplitude disturbances, this method cannot capture stability responses under finite-amplitude forcing conditions. Recent years have witnessed significant advancements in adjoint-based sensitivity analysis methods. By solving the adjoint equations of the flow system, this approach establishes gradient relationships between eigenvalues and variations in external inputs, thereby quantitatively evaluating the sensitivity of current flow stability states to external perturbations. This development has provided new dimensions for understanding flow instability mechanisms. This paper systematically reviews research progress in both global linear stability analysis and sensitivity analysis methods. The study first presents the theoretical framework of eigenvalue-equation-based linear stability analysis and adjoint-equation-based sensitivity analysis. Subsequently, it comprehensively examines four categories of external inputs affecting flow stability mechanisms: external perturbation forces, base flow forces decoupled from the flow field, base flow forces coupled with the flow field, and dimensionless parameters. Through progressive and multi-perspective analysis of their respective sensitivity gradient characteristics, the study reveals the underlying physical mechanisms and quantitative laws governing flow instability. The integration of linear stability analysis with adjoint sensitivity methods provides a more complete framework for understanding flow instability phenomena. This combined approach offers valuable insights for both theoretical research and practical applications in flow control, particularly in scenarios involving complex flow conditions and multiple influencing factors. These studies progressively unveil the physical mechanisms and quantitative laws governing flow instability through multi-perspective, layer-by-layer investigations.