This review focuses on identifying vital nodes in complex networks, which are crucial for controlling epidemic outbreaks, advertising, predicting scientific publications, and other applications. The paper discusses various methods for identifying vital nodes, including structural centralities, iterative refinement centralities, and dynamics-sensitive methods. It classifies these methods based on their use of structural information, local or global properties, and whether they consider dynamic processes. The review also covers weighted and bipartite networks, and evaluates the performance of different methods on various types of networks. It highlights the importance of identifying a set of vital nodes, which is more relevant to real-world applications than identifying individual nodes. The paper also discusses challenges in identifying vital nodes, such as the need for a universal index, the trade-off between local and global indices, and the difficulty of identifying a set of vital nodes. The review concludes with an outlook on future research directions in this field.This review focuses on identifying vital nodes in complex networks, which are crucial for controlling epidemic outbreaks, advertising, predicting scientific publications, and other applications. The paper discusses various methods for identifying vital nodes, including structural centralities, iterative refinement centralities, and dynamics-sensitive methods. It classifies these methods based on their use of structural information, local or global properties, and whether they consider dynamic processes. The review also covers weighted and bipartite networks, and evaluates the performance of different methods on various types of networks. It highlights the importance of identifying a set of vital nodes, which is more relevant to real-world applications than identifying individual nodes. The paper also discusses challenges in identifying vital nodes, such as the need for a universal index, the trade-off between local and global indices, and the difficulty of identifying a set of vital nodes. The review concludes with an outlook on future research directions in this field.