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Lateral stability of railway vehicle is a crucial aspect for railway vehicles. Primary critical speed, secondary critical speed, L/V ratio are the few measures of stability of railway vehicle. This paper reviews the linear and non-linear lateral stability analysis of railway vehicle. Various models presented by researchers for the analysis of vehicle stability in the past fifty years have been discussed. The major challenges faced by rail vehicle researchers for the accurate analysis of system stability have been briefly summarized in this article. The crucial parameters which influence the vehicle stability have been discussed in this paper.