Abstract: Thermoacoustic instability is a self-excited oscillatory phenomenon triggered by the mutual coupling between heat release rate fluctuations and acoustic oscillations in combustion systems. It is widely observed in energy and power equipment including gas turbines, aeroengines, industrial burners, and gas water heaters. Against the backdrop of low-carbon energy transition, the rapid growth in natural gas consumption and increasingly stringent nitrogen oxide emission standards have led combustion systems to frequently operate under low-emission conditions, for instance lean combustion and premixed modes, deviating from the stoichiometric ratio. This has resulted in frequent occurrences of thermoacoustic instability, manifesting as intense pressure oscillations, flame fluctuations, and increased noise, which severely compromise operational safety and equipment lifespan. This review systematically outlines recent research progress in oscillation mechanisms, triggering factors, nonlinear dynamic behaviors, current research status, and control strategies related to thermoacoustic instability in gas combustion. Starting from the classical Rayleigh criterion, the energy-positive-feedback mechanism of thermoacoustic coupling is explained. Typical oscillation types, among them Helmholtz-type, longitudinal modes, circumferential modes, and intrinsic thermoacoustic modes, are categorized and discussed in terms of their characteristics and causes. Regarding nonlinear behaviors, the physical mechanisms underlying dynamic phenomena like limit cycle oscillations, beating oscillations, and intermittent oscillations are further analyzed. Modeling approaches based on flame transfer functions and flame describing functions, together with their applications in predicting nonlinear oscillations, are also introduced. The review systematically summarizes current experimental diagnostic techniques in the field of gas thermoacoustic instability, encompassing high-frequency pressure measurements, particle image velocimetry, planer laser induced fluorescence, and chemiluminescence imaging, as well as numerical simulation methods including large eddy simulation, low-order network models, and Helmholtz solvers. Active and passive control strategies, for example acoustic dampers, fuel modulation, and plasma actuators, are also covered. Finally, challenges in current research and future development directions are discussed. It is emphasized that further breakthroughs are needed in areas such as combustion mechanisms of low-carbon fuels, multi-scale intelligent modeling, high-precision experimental diagnostics, and intelligent control to advance the design and optimization of low-emission, high-stability combustion systems.