  We overview some recent results in the field of uncertainty quantification
for kinetic equations and related problems with random inputs. Uncertainties
may be due to various reasons, such as lack of knowledge on the microscopic
interaction details or incomplete information at the boundaries or on the
initial data. These uncertainties contribute to the curse of dimensionality and
the development of efficient numerical methods is a challenge. After a brief
introduction on the main numerical techniques for uncertainty quantification in
partial differential equations, we focus our survey on some of the recent
progress on multi-fidelity methods and stochastic Galerkin methods for kinetic
equations.
