Evolutionary multitasking optimization focuses on population-based search and solving multiple tasks simultaneously via genetic transfer between tasks. It is considered as the third problem optimization paradigm after single-objective optimization and multiobjective optimization, and has become a hot research topic in the field of computational intelligence in recent years. The evolutionary multitasking optimization algorithm simulates the biocultural phenomena of assortative mating and vertical cultural transmission in nature, which leads to the improved convergence characteristics of multiple optimization tasks with inter-task and intra-task transfer knowledge. In this paper, we give a systematic review of the research progress in evolutionary multitasking in recent years. Firstly, the concept of evolutionary multitasking optimization is introduced and its related five definitions are given. We also explain this problem from the perspective of knowledge transfer optimization. Secondly, the basic framework of the evolutionary multitasking optimization algorithm is introduced in detail. The improvement of it and the implementation of other algorithms based on it are presented. Finally, the application in academic and engineering of this algorithm is summarized. At the end of this paper, we point out the existing challenges in the field of evolutionary multitasking optimization and make an outlook for the further development of this direction.