Abstract: Marangoni instabilities can emerge when a liquid interface is subjected to a temperature or concentration gradient. It has been extensively studied due to its wide relevance in industrial applications. It is generally believed that when it comes to Marangoni flows, bulk effects like buoyancy are negligible as compared to interfacial forces, especially on small scales. Consequently, the effect of a stable stratification on the Marangoni instability has been ignored. However, some recent researches have shown that even at small scales, the effect of stable stratifications cannot be ignored. This paper reviews the research progress on the Marangoni instability of a drop/bubble in a linearly stratified liquid. Two oscillatory instabilities, i.e., diffusion-limited instability and viscosity-limited instability are introduced, and the effect of advection, density stratification, diffusion, viscosity and container size on the instability are reviewed. Current results suggest that when the interface is not horizontal at small scales, the effect of a stable temperature/concentration gradient on the Marangoni flow and its instability may need reconsideration. Further research directions are suggested based on the current studies.