This paper provides a comprehensive review of techniques for identifying critical nodes in complex networks, which have become essential tools for understanding diverse phenomena, including social, transportation, biomolecular, and financial systems. Previous research has struggled to develop a universal framework for identifying critical nodes due to the inherent complexity and structural heterogeneity of real-world networks, including dynamic and high-order networks. This paper systematically categorizes critical node identification techniques into seven major categories: centrality, the critical node deletion problem, influence maximization, network control, artificial intelligence, and high-order and dynamic methods. This paper addresses the gaps in existing research by highlighting the strengths, limitations, and applicability of each method to various network types. Furthermore, it presents key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of high-order structures, and computational efficiency in large-scale networks, thereby enhancing our understanding of critical node research. Finally, it comprehensively summarizes current research progress, highlighting outstanding challenges, including temporal dynamics modeling, efficient algorithm development, integration of machine learning approaches, and development of scalable and interpretable metrics for complex systems.