Abstract: Lightweight materials are desired for energy saving and emission reduction of automobiles. A promising material for automobile parts is advanced high strength steel (AHSS). A recently developed material called medium-Mn steel, with excellent mechanical properties, has attracted increasing attention as the third-generation AHSS for automotive processing. However, medium-Mn steel is disadvantaged by plastic instability during tensile tests. This plastic instability is usually associated with localized and propagative bands on the material surface, which cause an unexpected surface roughening effect and premature failure in the most unfavorable cases. Therefore, plastic instability has severely impeded the commercialization of medium-Mn steels. The phenomenon manifests as discontinuous yielding followed by a yielding plateau (the Lüders strain), along with flow stress serrations (the Portevin-Le Chatelier (PLC) effect). Both effects are influenced by the composition, annealing process, and microstructure (phase morphology and constituents) of the steel. Both effects are also correlated with the austenite-to-martensite transformation during deformation to a greater or lesser extent, which is rarely observed in metallic materials. Consequently, the mechanisms of both effects are complicated and explainable by diverse theories. This paper reviewed the current research results on the influences of various factors on the Lüders strain and PLC effect, and discussed their corresponding mechanisms. This paper particularly emphasized the limitations of the existing theoretical explanations and proposed future researches to elucidate the existing disputes. Based on the current research and our preliminary experiment, this paper finally suggested ways of eliminating the plastic instability of medium-Mn steel, while guaranteeing ultrahigh strength, and excellent ductility. These improvements will drive the future development of this field.