Steel bars are prone to corrosion in harsh environments, resulting in degradation of mechanical properties of concrete members. Replacing steel bars with fiber reinforced polymer (FRP) stirrup can effectively avoid this problem. However, the low elastic modulus of FRP stirrup makes the beams easy to produce brittle shear failure. And the anisotropy makes the bending strength of FRP stirrup much lower than that of the straight section, resulting in the shear capacity of concrete beams with FRP rectangular stirrup being lower than that of reinforced concrete beams. In the past 20 years, in order to explore the practical application value of concrete beams with FRP rectangular stirrup, domestic and foreign scholars have carried out a series of experimental research and theoretical derivation, and put forward the calculation methods of shear bearing capacity and bending strength of FRP stirrup. In this paper, the above research results are summarized comprehensively, and the future research direction is prospected, in order to provide reference for the application and development of this kind of structural members.