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In the post-genomic era, proteomics has achieved significant theoretical and practical advances with the development of high-throughput technologies. Especially the rapid accumulation of protein-protein interactions (PPIs) provides a foundation for constructing protein interaction networks (PINs), which can furnish a new perspective for understanding cellular organizations, processes, and functions at network level. In this paper, we present a comprehensive survey on three main characteristics of PINs: centrality, modularity, and dynamics. 1) Different centrality measures, which are used to calculate the importance of proteins, are summarized based on the structural characteristics of PINs or on the basis of its integrated biological information; 2) Different modularity definitions and various clustering algorithms for predicting protein complexes or identifying functional modules are introduced; 3) The dynamics of proteins, PPIs and sub-networks are discussed, respectively. Finally, the main applications of PINs in the complex diseases are reviewed, and the challenges and future research directions are also discussed.