Most of engineering optimization problems can be formulated as constrained optimization problems. Evolutionary algorithms have been widely used in optimization constrained problems in recent years due to their sound performance. Nevertheless, the constraints make the solution space of the problem discrete, shrink and change, which bring great challenges to the evolutionary algorithm to solve the constrained optimization problem. The evolutionary algorithm integrating constraint handling technology has become a research hotspot. In addition, constraint processing techniques have been widely developed in the optimization of complex engineering application problems with the deepening of research in recent years, such as multi-objective, high-dimensional, equality constraint, etc. This study divides the evolutionary optimization for complex constraint optimization problems into evolutionary optimization algorithms for complex objectives and evolutionary algorithms for complex constraint scenarios according to the complexity. The challenges of constraint handling technology due to the complexity of practical engineering applications and the latest research progress in current research are discussed. Finally, the future research trends and challenges are summarized.