Abstract: Mathematical models of drying process are viewed as the primary basis for design of grain dryer, auto-control of drying operation and the optimization of drying technology. Crossflow drying is one of the methods widely used in grain drying. Three mathematical models for crossflow drying by researchers of USA were introduced in detail, including Bakker-Arkema PDE(Partial Differential Equation) model, two-dimensional dynamic PDE model, DP(Distributed Parameter) process model. Model predictive control method and its application in continuous crossflow grain dryer were also presented in this paper. All the introductions were aimed at providing some references for the similar research in our country.