The butterfly optimization algorithm (BOA) is a recent successful metaheuristic swarm-based optimization algorithm. The BOA has attracted scholars' attention due to its extraordinary features. Such as the few adaptive parameters to handle and the high balance between exploration and exploitation. Accordingly, the BOA has been extensively adapted for various optimization problems in different domains in a short period. Therefore, this paper reviews and summarizes the recently published studies that utilized the BOA for optimization problems. Initially, introductory information about the BOA is presented to illustrate the essential foundation and its relevant optimization concepts. In addition, the BOA inspiration and its mathematical model are provided with an illustrative example to prove its high capabilities. Subsequently, all reviewed studies are classified into three main classes based on the adaptation form, including original, modified, and hybridized. The main BOA applications are also thoroughly explained. Furthermore, the BOA advantages and drawbacks in dealing with optimization problems are analyzed. Finally, the paper is summarized in conclusion with the future directions that can be investigated further.