Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph reduction, or graph summarization, has gained prominence for simplifying large graphs while preserving essential properties. In this survey, we aim to provide a comprehensive understanding of graph reduction methods, including graph sparsification, graph coarsening, and graph condensation. Specifically, we establish a unified definition for these methods and introduce a hierarchical taxonomy to categorize the challenges they address. Our survey then systematically reviews the technical details of these methods and emphasizes their practical applications across diverse scenarios. Furthermore, we outline critical research directions to ensure the continued effectiveness of graph reduction techniques, as well as provide a comprehensive paper list at \url{https://github.com/Emory-Melody/awesome-graph-reduction}. We hope this survey will bridge literature gaps and propel the advancement of this promising field.