Abstract: Convection may occur in fluid because of the simultaneous buoyancy forces due to instability of gradients of two properties with different molecular diffusivity, which is usually called double-diffusive convection. It is a common phenomenon in nature and engineering. As more careful control and a higher quality manufacture are required for solidification processes of metallic alloys and semiconductor crystal growth, etc, double-diffusive convection problems have received more attention in recent years. The emphasis of this paper is on research work on double-diffusive convection with widely used models and methods, such as box models, two-dimensional Boussinesq model, k-e model, numericalmethods and some famous experimental methods.