The past two decades have borne remarkable progress in our understanding of flow mechanisms and numerical simulation approaches of shale gas reservoir, with much larger number of publications in recent 5 years compared to that before year 2012. In this paper, a review is constructed with three parts: flow mechanism, reservoir models and numerical approaches. In mechanism, it is found that gas adsorption process can be concluded into different isotherm models for various reservoir basins. Multi-component adsorption mechanisms are taken into account in recent years. Flow mechanism and equations vary with different Knudsen numbers, which could be figured out in two ways: molecular dynamics (MD) and lattice Boltzmann method (LBM). MD has been successfully applied in the study of adsorption, diffusion, displacement and other mechanisms. LBM has been introduced in the study of slippage, Knudsen diffusion and apparent permeability correction. The apparent permeability corrections are introduced to improve classic Darcy's model in matrix with low velocities and fractures with high velocities. At reservoir-scale simulation, gas flow models are presented with multiple porosity classified into organic matrix with nanopores, organic matrix with micropores, inorganic matrix and natural fractures. A popular trend is to incorporate geomechanism with flow model in order to better understand the shale gas production. Finally, to solve the new models based on enhanced flow mechanisms, improved macroscopic numerical approaches, including the finite difference method and finite element method, are commonly used in this area. Other approaches like finite volume method and fast matching method are also developed in recent years.