Abstract: Over more than two decades, research on simulation-based design under uncertainty has promoted the rigorous use of statistical analysis (data science) and probabilistic theory in engineering design. Novel algorithmic approaches have been developed to accelerate computational design innovation and optimization, and enable knowledge discovery in simulation-based design characterized by expensive multi-physics and multiscale simulations, high dimensionality, multi-modal data sources, and various sources of uncertainty. Recent years have seen a significant growth of using these methods for design of advanced materials systems. In this talk, we will introduce the success of using simulation-based design under uncertainty for designing both heterogeneous nano- and microstructural materials and architectural metamaterials, by integrating knowledge and representation from multiple disciplines and domains such as materials, manufacturing, structural mechanics, and design optimization. Challenges in design representation, design evaluation, and design synthesis associated with material systems will be introduced together with new techniques of microstructure characterization and reconstruction, multiscale uncertainty quantification and propagation, mixed-variable Gaussian process modeling, Bayesian optimization, and data-driven multiscale topology optimization.