Abstract: Mathematical models of crossflow grain drying and their applications were overviewed with the intention of providing some references for the similar research in our country. 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 applications in continuous crossflow grain dryer were also presented in this paper. DP process model, as a simplified form of PDE model, can perfectly simulate the drying process. DP model has simple analog computational procedure, being fitting for the online control of grain dryer. Based on the DP process model and MPC control algorithm, American researchers developed a model-predictive controller which was successfully applied on crossflow tower-dryer.