Butterfly optimization algorithm is a new metaheuristic algorithm, the idea of butterfly from foraging and courtship behavior. To further improve the search performance of butterfly optimization algorithm and speed up the research and application process of the algorithm, the principle, research status, comparison with other metaheuristic algorithms, and development trend of butterfly optimization algorithm are summarized. Firstly, the basic model of the algorithm is introduced. Then, combined with domestic and foreign literature, the variant algorithms are classified and described from the aspects of algorithm pa-rameters, chaos and quantum optimization, learning strategy, population diversity, and other improvement strategies. At the same time, the applications of butterfly optimization algorithm in the fields of image processing, wireless network, particle filter, photovoltaic system, medical system and other fields are classified. Next, the algorithm is compared with other metaheuristic algorithms in terms of advantages, disadvantages, and applicability. Finally, the future research and development direction of butterfly op-timization algorithm is prospected.