[Objective] Premixed flame stability is essential for the efficient, low -emission, and safe operation of gas turbines, aero-engines, industrial combustors, and distributed energy systems. With the increasing use of lean premixed combustion, hydrogen-enriched fuels, strong swirl stabilization, compact combustor designs, and thermal-boundary coupling, premixed flames have become more sensitive to local stretch, differential diffusion, wall heat loss, flow non -uniformity, and unsteady coherent s tructures. Conventional stability indicators, such as the limiting equivalence ratio and the critical flow velocity, can describe the global operating boundary of a combustor. However, they cannot adequately explain where instability is initiated, which lo cal mechanism dominates, or how local flame weakening develops into blow -off, flashback, or stabilization -mode transition. Therefore, premixed flame stability should be analyzed by linking global stability limits with local flame response and combustor-scale flow-thermal coupling. 

[Progress] This paper reviews the mechanisms and characterization methods of premixed flame stability. The theoretical basis is summarized from the perspectives of velocity matching, the Damkö hler number, flame stretch, flame curvature, Markstein response, Lewis -number effects, Karlovitz-number-based turbulent combustion regimes, and thermal-boundary coupling. These concepts show that flame stability is not governed by a single parameter. Instead, it depends on the balance among local flame propagation, residence time, strain rate, curvature, scalar dissipation, differential diffusion, and heat exchange. Turbulent premixed combustion regime diagrams provide a useful scale background for evaluating turbulence-flame interaction. However, global regime parameters should not be directly used as local extinction or flashback criteria, especially in flame roots, shear layers, recirculation -zone boundaries, and near -wall regions. Experimental methods are also reviewed, including particle image velocimetry, planar laser-induced fluorescence, high-speed chemiluminescence imaging, pressure measurement, wall -temperature measurement, and multimodal synchronized diagnostics. These methods help identify flame -root motion, recirculation -zone dynamics, local intermittency, heat-release oscillations, and near -limit transition pathways. Existing studies indicate that lean blow-off, flashback, and stabilization -mode transition usually do not result from simultaneous fail ure over the whole flame surface. They are more often caused by the accumulation of local events, including reaction weakening, flame -root detachment, local extinction, downstream residual reaction, hot -product recirculation, intermittent re -ignition, and final re -ignition failure. The roles of direct numerical simulation, large eddy simulation, and conjugate heat transfer simulation are further discussed. Direct numerical simulation is suitable for resolving detailed chemistry, molecular transport, scalar dissipation, local extinction, re -ignition, and radical transport in canonical flames. Large eddy simulation is useful for predicting coherent structures, flame -root dynamics, heat-release oscillations, and near-blow-off behavior in practical combustors. Its reliability depends on subgrid combustion models, inlet turbulence, grid resolution, chemical mechanisms, and wall-boundary treatment. Conjugate heat transfer simulation extends stability analysis to solid conduction, wall heat flux, stabilizer temperature, and thermal feedback. It is important for compact combustors and near -wall flame stabilization. 

[Conclusion] Premixed flame stability is controlled by the competition between local reaction -sustaining capability and flow -induced stretch, mixing dissip ation, residence time, differential diffusion, and heat loss. Global stability boundaries should be understood as the macroscopic outcome of local flame response and combustor-scale flow -thermal coupling. Future studies should establish cross -scale relatio nships between local instability indicators and global stability limits. Experimental validation using multimodal diagnostics should be strengthened. Numerical modeling frameworks based on direct numerical simulation, large eddy simulation, and conjugate h eat transfer simulation should also be further improved. These efforts will support the prediction, characterization, and control of premixed flame stability in complex low-emission combustors.