Reptile Search Algorithm (RSA) is a recently developed nature-inspired meta-heuristics optimization algorithm inspired by the encircling mechanism, hunting mechanism and social behaviours of crocodiles in nature. Since Abualigah et al. introduced RSA in 2022, it has garnered significant interest from researchers and been widely employed to address various optimization challenges across a variety of fields. This is because it has an adequate execution time, an efficient convergence rate, and is more effective than other well-known optimization algorithms. As a result, the objective of this study is to provide an updated survey on the topic. This study provides a comprehensive report of the classical RSA, and its improved variants and their applications in various domains. To adequately analyse RSA, a comprehensive comparison among RSA and its peer NIOAs is performed using mathematical benchmark functions.