The next generation of complex engineered systems will be endowed with sensors and computing capabilities that enable new design concepts and new modes of decision-making. For example, new sensing capabilities on aircraft will be exploited to assimilate data on system state, make inferences about system health, and issue predictions on future vehicle behavior—with quantified uncertainties—to support critical operational decisions. However, data alone is not sufficient to support this kind of decision-making; our approaches must exploit the synergies of physics-based predictive modeling and dynamic data. This talk describes our recent work in adaptive and multifidelity methods for optimization under uncertainty of large-scale problems in engineering design. We combine traditional projection-based model reduction methods with machine learning methods, to create data-driven adaptive reduced models. We develop multifidelity formulations to exploit a rich set of information sources, using cheap approximate models as much as possible while maintaining the quality of higher-fidelity estimates and associated guarantees of convergence.