In this talk, I will present some recent work on high-dimensional learning of complex models and model-constrained optimization (of control, design, and experiment) under uncertainty to create digital twin of physical systems. Tremendous computational challenges are faced for such problems when (1) the models (e.g., described by partial differential equations) are expensive to solve and have to be solved many times or in real time; and (2) the data, optimization, and uncertain variables are high-dimensional, bringing the curse of dimensionality for most conventional methods. We tackle these challenges by exploiting both data and model informed properties, such as smoothness, sparsity, correlation, intrinsic low-dimensionality or low-rankness, etc. I will present several new computational methods that achieve significant computational reduction (fast) and break the curse of dimensionality (scalable), including structure-exploiting model reduction, randomized high-order tensor decomposition, derivative informed deep learning, projected transport map, and functional Taylor approximations. I will also briefly talk about some applications of these methods in learning and optimal mitigation of infectious disease (COVID-19), optimal control of turbulent combustion, optimal design of stellarator for plasma fusion, and optimal experimental design for sensor placement.