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Graph neural networks have emerged as a leading architecture for many graph-level tasks, such as graph classification and graph generation. As an essential component of the architecture, graph pooling is indispensable for obtaining a holistic graph-level representation of the whole graph. Although a great variety of methods have been proposed in this promising and fast-developing research field, to the best of our knowledge, little effort has been made to systematically summarize these works. To set the stage for the development of future works, in this paper, we attempt to fill this gap by providing a broad review of recent methods for graph pooling. Specifically, 1) we first propose a taxonomy of existing graph pooling methods with a mathematical summary for each category; 2) then, we provide an overview of the libraries related to graph pooling, including the commonly used datasets, model architectures for downstream tasks, and open-source implementations; 3) next, we further outline the applications that incorporate the idea of graph pooling in a variety of domains; 4) finally, we discuss certain critical challenges facing current studies and share our insights on future potential directions for research on the improvement of graph pooling.