Abstract: The non-convex minimax problem is an important research front and hot spot in the cross-fields of optimization, machine learning, signal processing, etc.. Some key scientific issues in frontier research directions such as adversarial learning, reinforcement learning, and distributed non-convex optimization, all belongs to this type of problem. Internationally, the research on convex-concave minimax problems has achieved good results. However, the non-convex minimax problem is different from the convex-concave minimax problem, and it is a non-convex and non-smooth optimization problem with its own structure, for which, the theoretical analysis and the algorithm design are more challenging then that of the convex-concave minimax problem, and it is generally NP-hard. This paper focuses on the latest developments in optimization algorithms and complexity analysis for non-convex minimax problems.