The development of high-energy density and high-safety all-solid-state lithium battery (ASSLB) technology has important practical significance for promoting the upgrading of lithium battery technology and the strengthening of technological development in this field. The solid electrolyte is a core component of the ASSLB. The sulfide solid electrolyte is regarded as one of the most promising solid electrolyte candidates for practical application in ASSLBs due to its high ionic conductivity, better mechanical ductility, and good interface contact with the electrode. However, its practical application is severely hampered by the issues of poor air stability and interface problems, including interface side reactions, lithium dendritic growth, and interface mechanical failure. In this review, we first summarize the research methods and degradation mechanisms of the air stability of sulfide solid electrolytes, and the strategies and methods to improve their air stability. Then, the electrochemical stability, interface compatibility and related interfacial modification strategies for sulfide electrolyte/electrode interface are summarized and discussed. Further, the research progress of in-situ characterization technologies for sulfide solid electrolyte/electrode interfaces in recent years is analyzed and summarized. Finally, an outlook on the future research and development of stable interfaces in sulfide solid electrolyte based ASSLBs is highlighted.