Constrained optimization evolutionary algorithm, which mainly studies how to use evolutionary computation method to solve constrained optimization problems, is an important research topic in evolutionary computation field. Discrete constraint, equality constraint, nonlinear constraints are challenges to solving constraint optimization. The basis of this problem solving is how to handle the relationship between feasible solution and infeasible solution. In this study, the definition of constrained optimization problem is firstly provided, and then, the existing constrained optimization approaches are systematically analyzed. Meanwhile, algorithms are classified into six categories (i.e., penalty function method, feasible rules, stochastic ranking, ε-constraint, multi-objective constraint handling, and hybrid method), and the state-of-art constrained optimization evolutionary algorithms (COEAs) are surveyed with respect to constraint-handling techniques. Research progress and challenges of the six categories of constraint handling techniques are discussed in detail. Finally, the issues and research directions of constraint handling techniques are discussed.