An accurate description of fluid flow is critical for the prediction of the productivity of shale gas reservoirs. In this paper, we present the current advances and a systematic summary on the fluid flow in shale gas reservoirs. First, shale pore structures, consisting of organic pores and inorganic pores ranging from nanoscale to micro-scale, and reservoir fluids, including free gas, absorbed gas, and water, are systematically presented. Thereafter, multi-physics flow phenomena motivated by scale effects, such as continuum flow, slip flow, transition flow, free molecular flow, and surface diffusion for gas, as well as the effective viscosity and slip boundary condition for water, are carefully summarized. Meanwhile, these flow mechanisms are discussed with molecular dynamics (MD) simulations and theoretical analysis. Subsequently, on the basis of upscaling approaches, including capillary bundle models, the lattice Boltzmann method (LBM), and pore network models (PNMs), fluid flow through heterogeneous shale matrix is reviewed and the influences of scale effects and pore structures are clarified. Additionally, shale gas well performance is discussed by combining the multiple transport mechanisms and a fracturing-shut-in-flowback-production process. Our review concluded that the fluid flow behaviour in shale gas reservoirs is a complex multi-scale process accompanied by multi-physical phenomena and multi-fluid distributions. Keeping this in mind is helpful for predicting the shale gas production and recoverable gas resources. We expect this study can not only help by providing a better understanding of the fluid flow in shale reservoirs but also provide significant implications to address other multiphase flow processes.