Michael Eldred - Sandia National Laboratories Computational simulation continues to advance in its predictive capability through the development of high-fidelity multi-scale / multi-physics simulation models executing on the latest high-performance computers. UQ methodologies are challenged in this environment, both by the prohibitive cost of computing high-fidelity ensembles and by the increasing random dimensionality induced by this model complexity. To address these challenges, new algorithmic approaches are harnessing the utility that exists within hierarchies of model forms (multifidelity) and discretization levels (multilevel). In this presentation, we focus on the development and deployment of multilevel-multifidelity (ML-MF) algorithms that adaptively fuse information from multiple sources in order to reduce the overall computational burden. In particular, we focus on forward UQ using ML-MF Monte Carlo sampling, for use in high-dimensional problems of limited regularity, and ML-MF polynomial expansion approaches, for use in exploiting sparse and low rank structure in smooth problems. Several approaches for adaptively allocating samples across levels will be explored and compared, based on deployments to both standard model problems and engineered aerodynamic systems.