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In this talk, we will introduce the recent advance on the multiscale computation for the electromagnetic field in heterogeneous materials such as quantum dots, CMOS transistor, photonic crystal and so forth.First, we briefly survey the theoretical results of the homogenization method and the multiscale method for macroscopic Maxwells equations in heterogeneous materials.Second, we study the Schroedinger equations with the effective mass approximation which has been particularly successful in the case of heterostructures.We offer a interpretation why the effective mass approximation is very successful for calculating the band structures of semiconductor nanostructures in the vicinity of Γ point, from the viewpoint of mathematics.Third, we analyze the relationship between microscopic Maxwells equations and macroscopic Maxwells equations.Furthermore, we discuss mathematical modeling of electromagnetics at nano-scale and give an explanation as to why Schroedinger-Poisson equations and Maxwell-Schroedinger equations have been widely used to semiconductor nanostructures.Fourth, the multiscale method for Schroedinger-Poisson system in heterogeneous materials is presented.Numerical simulations are carried out to validate the theoretical results.Finally, some unsolved problems are advanced.