The goal of this paper is to compare the similarities and differences between Bayesian and belief function reasoning. Our main conclusion is that although there are obvious differences in semantics, representations, the rules for combining and marginalizing representations, there are many similarities. We claim that the two calculi have roughly the same expressive power. Each calculus has its own semantics that allow us to construct models suited for these semantics. Once we have a model in either calculus, one can transform it to the other by means of a suitable transformation.