Machine learning (ML) techniques have been widely employed as effective tools in addressing various engineering challenges in recent years, particularly for the challenging task of microstructure-informed materials modeling. This work provides a comprehensive review of the current ML-assisted and data-driven advancements in this field, including microstructure characterization and reconstruction, multiscale simulation, correlations among process, microstructure, and properties, as well as microstructure optimization and inverse design. It outlines the achievements of existing research through best practices and suggests potential avenues for future investigations. Moreover, it prepares the readers with educative instructions of basic knowledge and an overview on ML, microstructure descriptors, and ML-assisted material modeling, lowering the interdisciplinary hurdles. It should help to stimulate and attract more research attention to the rapidly growing field of ML-based modeling and design of microstructured materials. Graphical abstract