Steel reinforcements in concrete tend to corrode and this process can lead to structural damage. Fiber-reinforced polymer (FRP) reinforcements represent a viable alternative for structures exposed to aggressive environments and have many possible applications where superior corrosion resistance properties are required. The use of FRP rebars as internal reinforcements for concrete, however, is limited to specific structural elements and does not yet extend to the whole structure. The reason for this relates to the limited availability of curved or shaped reinforcing FRP elements on the market, as well as their reduced structural performance. This article presents a state-of-the art review on the strength degradation of curved FRP composites, and also assesses the performance of existing predictive models for the bend capacity of FRP reinforcements. Previous research has shown that the mechanical performance of bent portions of FRP bars significantly reduces under a multiaxial combination of stresses. Indeed, the tensile strength of bent FRP bars can be as low as 25% of the maximum tensile strength developed in a straight counterpart. In a significant number of cases, the current design recommendations for concrete structures reinforced with FRP were found to overestimate the bend capacity of FRP bars. A more accurate and practical predictive model based on the Tsai–Hill failure criteria is also discussed. This review article also identifies potential challenges and future directions of research for exploring the use of curved/shaped FRP composites in civil engineering applications.