This paper reviews the previous work on multiscale simulations of linear and non-linear problems in polycrystalline functional materials.The motivation of this study is to understand the complicated relation between macroscopic homogenized physical property and microscopic inhomogeneous crystal morphology.It will lead the microstructural design for enhancement of physical property.The asymptotic homogenization theory is employed for scale-bridging.First,two tpoics in displacement-electric potensial coupling linear problems are introduced for polycrystalline BaTiO3.One is a multiscale simulation based on realistic microstructure model which were constructued from EBSD-meseared crystal orientations.We discuss about the influence of microstructural sampling area on macroscopic homogenized physical properties,and the comparison between two-and three-dimensional microstructure models.The other is the optimization of microstructural crusyal morphology to miximize the macroscopic homogenized piezoelectric response.This analysis reveals that two specific microstructures,layered or alternating[111]-oriented structures,result in a piezoelectric strain constant d333 or d3u that exceeds that of the single crystal.Second,the application of multiscale simulation to nonlinear problems is proposed for ferroelectfic hysteresis behaviours caused by domain switching.We utilize an incremental form of fundamental constitutive law in consideration with physical property change caused by domain switching.The nonlinear behaviors of polyerystalline ferroelectrics with textured mierostructure are analyzed for case study.The influence of crystal orientation distribution on macroscopic hysteresis and butterfly curves are revealed.