In this chapter, we introduce the concepts of distributions and random variables in CUQIpy, and how to use them to define priors for Bayesian inverse problems. We also showcase a collection of predefined distributions intended for testing sampling algorithms. Additionally, we provide an overview of implicit priors in CUQIpy. Note that the subject of hierarchical priors is left for chapter Chapter 9: Hybrid Gibbs sampling in CUQIpy, where we introduce the hybrid Gibbs sampling framework in CUQIpy.