Combinatorial optimization problems (COPs) are a class of optimization problems that are commonly encountered in industrial production and everyday life. Over the last few decades, traditional algorithms, such as exact algorithms, approximate algorithms, and heuristic algorithms, have been proposed to solve COPs. However, as COPs in the real world become more complex, traditional algorithms struggle to generate optimal solutions in a limited amount of time. Since Deep Neural Networks (DNNs) are not heavily dependent on expert knowledge and are adequately flexible for generalization to various COPs, several DNN-based algorithms have been proposed in the last ten years for solving COPs. Herein, we categorize these algorithms into four classes and provide a brief overview of their applications in real-world problems.