The purpose of this hands-on tutorial is to expose participants to statistical and numerical techniques that will allow them to quantify the accuracy of multi-physics models and simulation codes for active materials and structures when one accounts for uncertainty or errors in models, parameters, numerical simulation codes, and data. Additionally, we will discuss global sensitivity analysis techniques for parameters, as well as uncertainty propagation techniques, and illustrate how they provide insights regarding material behavior and can be used to quantify the accuracy of predictions.<br/> In the first part of the tutorial, we will provide an overview of Bayesian statistics, sensitivity analysis methodologies, and numerical algorithms necessary to propagate input uncertainties through simulation codes. We will consider several case studies to illustrate these techniques for a variety of materials and smart structure applications. These include models for piezoelectric macro-fiber composites, shape memory alloys, viscoelastic polymers, graphene thermoacoustics, quantum-informed ferroelectric continuum models, and Rietveld analysis. In this part of the tutorial, we will provide participants with algorithms that quantify the uncertainties in model parameters, such as piezoelectric constants, when they are calibrated from experimental data. We will show how global sensitivity analysis can be used to rank model parameters and isolate those parameters that cannot be reliably estimated from data. To illustrate the uncertainty propagation techniques, we will demonstrate the construction of 95% prediction intervals for PZT models at a given applied field. Finally, we will demonstrate, in the context of a shape memory alloy example, the manner in which robust control designs can be improved through uncertainty quantification.<br/> In the second, hands-on, part of the tutorial, we will have participants run case studies using MATLAB. These studies will include models and data provided by the instructors, but participants are also encouraged to bring their own models and data for testing during the tutorial, based on their specific problem(s) of interest.