Near-surface mounted (NSM) fiber-reinforced polymer (FRP) technique is known as a promising alternative to the externally bonded (EB) FRP technique for strengthening reinforced concrete (RC) members, on account of its many advantages such as high bond efficiency with concrete and good durability. Shear strengthening of RC beams by near-surface mounting the FRP bars/strips into the concrete cover on beam sides is one of the most prevalent applications of NSM FRP. Abundant experimental studies have been conducted to investigate the behaviour of NSM FRP shear strengthened beams, and many strength models for predicting the contribution of NSM FRPs to the shear capacity of the beam have been proposed. The present paper presents a comprehensive review of these strength models, in which all the models collected from the existing literature are first classified into three categories based on their used approach and then summarized and discussed. This paper not only aims to bring a deep understanding of the existing strength models for NSM FRP shear strengthened RC beams, but also provides a background and basis for the assessment of these models by using the newly-generated experimental database in the companion paper.