More and more experimental results show that Darcy's law is not fully applicable in low permeability media, and non-Darcy flow has been identified. In this paper we reviewed the research of non-Darcy flow experiments in low-permeability media in recent decades, discuss the existence of non-Darcy flow, and summarize its constitutive equations. The reasons for the threshold gradient were also discussed and summarized for the criterion of the critical point of non-Darcy flow. On this basis, the future development of non-Darcy flow experiments in the rock and clay media were discussed, in order to provide a certain reference for subsequent research on seepage laws in low permeability media.