Liquefied natural gas (LNG), as cleaner transitional energy than coal, is becoming increasingly prominent in the energy structure of various countries based on their low-carbon background, and its demand has grown rapidly worldwide. Storage tanks are the most commonly used LNG storage facilities. Owing to a variety of internal composition and external environmental factors, the instability phenomenon of LNG in the tanks may occur during storage, leading to potential safety risks. An in-depth understanding of the stratification and rollover behavior of LNG is therefore required to ensure and promote efficient utilization and stable storage of LNG. This paper provides a comprehensive review of the current state of LNG stratification and rollover behavior. The factors for causing LNG stratification and rollover behavior in the storage tanks are summarized, methods for characterizing stratification and rollover behavior are discussed, and measures for inhibiting the instability phenomenon of LNG in the tanks are highlighted. Future researchers should conduct further work in enriching the factors affecting the stratification and rollover behavior, improving characterization methods, and developing inhibition measures to ensure the safe and stable storage of LNG.