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Building sensible processing-structure-property (PSP) links to gain fundamental insights and understanding of materials behavior has been the focus of many works in computational materials science. Microstructure characterization and reconstruction (MCR), coupled with machine learning techniques and materials modeling and simulation, is an important component of discovering PSP relations and inverse material design in the era of high-throughput computational materials science. In this article, we provide a comprehensive review of representative approaches for MCR and elaborate on their algorithmic details, computational costs, and how they fit into the PSP mapping problems. Multiple categories of MCR methods relying on statistical functions (such as n-point correlation functions), physical descriptors, spectral density function, texture synthesis, and supervised/unsupervised learning are reviewed. As no …