<p>Nonlinear equation systems (NESs) are widely prevalent in various practical applications, such as those in physics, engineering, chemistry, and economics. Solving NESs is an important research topic in the optimization community. Meta-heuristic algorithms (MAs) have proven effective in dealing with various real-world optimization problems. During the past ten years, using MAs to solve NESs has become an important research direction. This work aims to comprehensively review the MAs that have been utilized to solve NESs. First, the concept of NES is briefly elucidated. Then, based on the basic frameworks of MAs for solving nonlinear equations, the research progress of state-of-the-art algorithms for NESs is summarized from the two aspects of transformation methods and MAs. Subsequently, the benchmark test problems and evaluation metrics of NESs are introduced and the performance of ten representative state-of-the-art MAs is compared, meanwhile, the discussions of NESs based on real-world problems and applications are presented. Furthermore, the urgent problems that need to be solved by using MAs to deal with NESs are analyzed. Finally, the open research issues in this community are summarized.</p>