The transport property of granular material that is a typical of soft matter, plays a significant role in durability and service life in a relevant practical engineering structure. Physical properties of material is generally dependent on its microstructure. Meanwhile, the formation of microstructure is directly related to compositions of granular material. Understanding the intrinsic mechanisms of composition, microstructure, and transport property are of great importance for improving mechanical properties and durability of granular material. In this article, we review the new progress of modeling transport properties of granular multiphase materials. We focus on the three main aspects involving the simulations for geometrical models of composition structures, the quantitative characterizations for microstructures of pore and interface phases, and the theoretical and numerical strategies for transport properties of granular multiphase materials. In the first aspect, in-depth reviews of realizing complex morphologies of geometrical particles, detecting the overlap between adjacent non-spherical particles, and packing randomly non-spherical particles are presented. In the second aspect, we emphasize the development progress of the interfacial thickness and porosity distribution, the interfacial volume fraction, and the continuum percolation of soft particles such as compliant interfaces and discrete pores. In the final aspect, the modeling the transport properties and the frontier issues of the effective diffusion and anomalous diffusion in granular multiphase materials are elucidated. Finally, some conclusions and perspectives for future studies are provided.