This paper explains the necessity of the study on flow motion law in leaky aquifer system and reviewed its research status at home and abroad. Then, it discusses the research methods and model building in leaky aquifer systems, the existence and criterions of non-Darcy flow in low permeability media, and the related models and equations for non-Darcy flow in low permeability media. Finally, it points out that the coupling of the leakage and non-Darcy flow in low permeability media is one of the most important development directions of the study on flow motion law in leaky aquifer system in future. The influences of non-Darcy flow, consolidation, and elastic storage and release on flow in leaky aquifer system need to be studied from a spatio-temporal perspective.