**作者：**FALIN CHEN**中文摘要：**In the present review article, we discuss recent progress in stability analysis of the convection of binary solutions which are solidified uni-directionally. Several double-diffusive convective flows with various stability characteristics occur either in sequence or simultaneously in a system, thus affecting seriously the crystalline of the resultant casting. Similar convective flows are also found in, for example, the Earth is inner core, the magma chamber, the polar ocean, and so on. A number of experimental results are first introduced to illustrate the flow structure as well as the convection phenomena. An extensive discussion of the theoretical model is then provided. Special attention is paid to the stability characteristics of each convective flow, which may be of fundamental interest to fluid mechanics researchers. Special cases based on effects due to some physical parameters are provided. Finally, the difficulties encountered in previous investigations are discussed, and some potential problems meriting further research are proposed.**英文摘要：**--**中文關鍵字：**directional solidification, double-diffusive, hydrodynamics stability**英文關鍵字：**--