Real-world engineering design problems are widespread in various research disciplines in both industry and industry. Many optimization algorithms have been employed to address these kinds of problems. However, the algorithm’s performance substantially reduces with the increase in the scale and difficulty of problems. Various versions of the optimization methods have been proposed to address the engineering design problems in the literature efficiently. In this paper, a comprehensive review of the meta-heuristic optimization methods that have been used to solve engineering design problems is proposed. We use six main keywords in collecting the data (meta-heuristic, optimization, algorithm, engineering, design, and problems). It is worth mentioning that there is no survey or comparative analysis paper on this topic available in the literature to the best of our knowledge. The state-of-the-art methods are presented in detail over several categories, including basic, modified, and hybrid methods. Moreover, we present the results of the state-of-the-art methods in this domain to figure out which version of optimization methods performs better in solving the problems studied. Finally, we provide remarkable future research directions for the potential methods. This work covers the main important topics in the engineering and artificial intelligence domain. It presents a large number of published works in the literature related to the meta-heuristic optimization methods in solving various engineering design problems. Future researches can depend on this review to explore the literature on meta-heuristic optimization methods and engineering design problems.