Abstract: The progresses in researches of the convective instabilities arereviewed in this paper. First, the analyses of the instabilities of the classicone layer model are introduced. Where the dynamic coupling between the vaporlayer and the liquid layer is not considered, so evaporatinginstabilities could not be explained. In order to introduce the dynamiccoupling between the vapor layer and the liquid layer, two sided modelswith an evaporating interface were proposed. The assumption of the continuity of thetemperature at the interface is usually adopted. However, thetemperature at the evaporating interface was found discontinuous inexperiments, especially when the evaporating flux is large. Because theassumption of the continuity of the temperature is not true in anon-equilibrium system, these models can not explain theMarangoni-B{\'e}nard instabilities of the evaporating layer,especially when the liquid layer is cooled from below. Thispaper reviews previous research results and dynamic models.We discuss the Marangoni-B{\'e}nard instabilities of thesemodels, and point out some open problems for future researches.