Shape Memory Alloys (SMAs) are an innovative material with the unique features of superelasticity and energy dissipation capabilities under extreme loads. Due to their unique features, they have a great potential to be employed in structural engineering applications under different conditions. However, in order to effectively use SMAs in civil engineering structures and model their behaviors accurately in Finite Element (FE) packages, it is crucial for structural engineers to comprehend the mechanical properties and cyclic behavior of different SMA compositions under varying loading conditions. While previous studies have focused mainly on the cyclic behavior of SMAs under tensile loading, it is important to evaluate their fatigue behavior under cyclic tension-compression loading for seismic applications. This literature review aims to discuss the current gaps in the existing literature on the behavior of SMA rebars under low-cycle fatigue (LCF). The review provides a comprehensive overview of the primary characteristics of SMAs, summarizes the mechanical properties of SMAs presented in the literature and the parameters that affect them, and critically evaluates the effects of cyclic loading and LCF on SMAs. The review also provides a summary of the different constitutive models of SMAs and compares their advantages and limitations, which helps structural engineers to employ an appropriate constitutive model for predicting the accurate behavior of SMAs in FE software.