This thesis describes experiments on few-body interactions in a mixture of ultracold bosonic 87Rb and fermionic 40K atoms. Ultracold atoms are celebrated as a platform to explore fundamental quantum physics because their internal states, external potentials, and interactions with each other can be controlled by straightforward electrical and optical tools. In the case of Bose-Fermi mixtures, control comes at the cost of stability when strong interactions give rise to inelastic collisions that destroy the atomic samples. I present detailed measurements of the cross sections for these inelastic processes and discuss how they fit into an emerging pattern of resonances that is leading to better models of few-atom interactions. These phenomena have their roots in universal Efimov physics, which is a paradigm of quantum three-body interactions that was originally inspired by exotic nuclear states. I also discuss several methods to control the formation of KRb Feshbach molecules within the finite lifetime of the interacting K and Rb atomic mixture.