4 June 2021 In this talk I will cover numerical techniques for quantifying parametric uncertainties in hyperbolic problems (e.g., fluid flow, kinetic models, etc.) where we change the underlying equations to include uncertain dimensions. Upon discretizing the resulting equations we obtain an approximation of the solution including the uncertainty in the solution. One aspect of these approaches is that the behavior of the solutions can change, such as shocks no longer sharp. Additionally, when using a continuous basis for the uncertain dimensions such as polynomial chaos, the resulting equations can exhibit spurious oscillations. I will discuss approaches to tackle these oscillations and demonstrate that techniques developed in kinetic theory can be transferred to intrusive UQ. Numerical experiments will convey the effectiveness of these approaches.