This paper comprehensively reviews the mainly famous and important literature about equity risk premium (ERP)puzzle. From the long term perspective,most markets show the equity yields surprisingly high return,and the discrepancy between the return of equity and risk free rate cannot be explained by any classical equilibrium models. The paper is divided into five parts. The first three parts review vast literature about the discovery and development of ERP puzzle. Most literature conducted on the development of quantitative model and qualitative theories briefly point out their failures of explaining ERP puzzle. The fourthpart shows the empirical studies about ERP puzzle among international countries and the robustness of testing methods. The last partis the brief conclusion of the paper and the prospectsof ERP puzzle.