Abstract: Dynamic multi-objective optimization problems widely occur in real-world production and life. Their characteristics change over time or vary with environments. To solve these problems effectively, researchers proposed two kinds of problem solvers, namely, dynamic multi-objective evolutionary optimization methods to track optimal solutions and robust dynamic multi-objective evolutionary optimization methods to search for robust Pareto-optimal solutions. In the first kind, optimization is retriggered after dynamic changes in the characteristics of multi-objective optimization problems are detected. This process aims to converge to real Pareto fronts of optimization problems in a new environment quickly and accurately. Thus, the mechanisms of detecting an environmental change and the corresponding response strategies are essential. In this paper, we classify and summarize previous studies on environmental detection methods and response strategies, including diversity preservation, memory, prediction mechanism, and transfer learning. To reduce the switching cost among solutions effectively and provide feasible and satisfactory optimal solutions for users in a limited time, we construct a new robust multi-objective optimization model through robust dynamic multi-objective evolutionary optimization and develop robust Pareto-optimal solutions. Results reveal that the proposed model has an optimal convergence performance under the current environment and approaches the true Pareto fronts of optimization problems in several subsequent future dynamic environment with the satisfied threshold. We also provide a series of commonly used indicators to evaluate two kinds of above-mentioned algorithm performence. Lastly, we emphasize the difficulties and challenges in dynamic multi-objective evolutionary optimization through an analysis of the limitations of existing methods.