Solving nonlinear equation systems is an important research topic in optimization field. In recent years, using intelligent optimization algorithms to solve nonlinear equation systems has become an important research area. In this paper, the definition of nonlinear equation systems is firstly introduced. And then, based on the basic principles of intelligent optimization algorithms for solving nonlinear equations, state-of-the-art algorithms of solving nonlinear equation systems are surveyed from the aspects of transformation methods and intelligent optimization algorithms. In addition, the benchmark test functions and performance criteria of nonlinear equation systems are described, and the performances of five representative algorithms are compared, meanwhile, the problems that need to be solved are analyzed. Finally, the open research issues in this field are pointed out.