A digital twin is an evolving virtual model that mirrors an individual physical asset throughout its lifecycle. Key to the digital twin concept is the ability to sense, collect, analyze, and learn from the asset’s data. This talk will highlight the foundational mathematical, statistical and computational challenges that must be overcome to achieve predictive digital twins for societally critical applications across science and engineering. Digital twins hold the promise to underpin intelligent automation by supporting data-driven decision making and enabling asset-specific analysis, but this can only be achieved through a synergistic combination of predictive physics-based modeling, data-driven machine learning, and uncertainty quantification.