Metaheuristic optimization methods are extensively employed to address complex real-world problems, but problems like premature convergence and poor search persist. Reptile Search Algorithm (RSA) is a new nature-inspired optimization method founded on the cooperative hunting strategy of crocodiles. This review offers an in-depth examination of RSA, examining its theoretical roots, mathematical modelling, and relative performance compared to established methods such as PSO, GWO, and WOA. The novel encircling and hunting mechanisms of the algorithm provide a balance between exploration and exploitation, increasing global search efficiency. Performance tests on benchmark problems and engineering problems prove RSA's strength, flexibility, and performance in multimodal and high-dimensional problems. In real-world applications, RSA has been effectively applied to machine learning, engineering design, and industrial optimization. RSA indicates promising outcomes but parameter tuning and hybridization with other techniques remain challenging. Future work should target adaptive methods, parallel execution, and domain-specific optimization to make it more applicable in various areas.