In this work, a comprehensive review of the multi-objective grey wolf optimizer (MOGWO) is provided. In multi-objective optimization (MO), more than one objective function must be considered at the same time. To deal with such problems, a priori or a posteriori MOGWO variants have been proposed in the literature. In the a priori model, the multi-objective functions are aggregated into a single objective function by a number of weights. In the posterior model, the multi-objective formulation is maintained and MOGWO is employed to estimate the Pareto optimal solutions representing the best trade-offs between the objectives. Due to the successful performance of MOGWO, it has been widely utilized for MO. This review covers the research growth of MOGWO in terms of a number of researches, topics, top researchers, etc. Furthermore, several versions of MOGWO have been introduced and reviewed with applications in diverse fields. This work also provides a critical analysis to show the shortcomings and limitations of using the basic version of MOGWO followed by several future directions. This review paper will be a base paper for any researcher interested to implement MOGWO in its work.