This EUROMECH colloquium focuses on recent advances in the field of data-driven microstructure modeling and addresses a wide type of materials and applications: porous, composite and polycrystalline media, mechanical and transport properties. In particular, contributions related to machine learning and stochastic microstructure modeling, generation of digital twins, numerical simulation of effective properties, AI-based methods for characterizing, predicting or optimizing mechanical and transport properties, as well as elucidating process-microstructure and microstructure-property relationships are welcome. A special focus of the colloquium is on modeling with applications to electro-chemical devices.