The understanding of structural and property relationship in functional materials is often limited by the static and spatially-averaged characterization methods. Probing materials in 4D space-time dimensions with high precision is the foundation to modern materials research. The recent advances in ultrafast optics, aberration-correction electron beam and synchrotron X-ray techniques provide new opportunities in developing the next-generation materials characterization methods. By combining computational imaging with advanced electromagnetic probes, this project aims at developing high-precision, low-dosage, light-element sensitive characterization methods, as well as focusing on solving long-standing  problems in functional materials.