This lecture will outline a probabilistic framework for uncertainty quantification, and will discuss applications of associated methods and algorithms for the purpose of calibrating physical parameters from measured data, model selection, and design of experiments so as to optimize information about specific observables. Concepts will be illustrated in light of specific applications to nanofluidics and energetic materials. One of the central goals of the lecture will be highlight the importance of proper setup of the “UQ problem,” which generally necessitates judicious combination of information originating from diverse disciplines.