The complexity of many biological processes often leads to models that naturally contain many quantitative parameters. These parameters are often poorly known a priori and difficult to infer via fitting. In the first part of the talk, I will discuss Bayesian approaches to grappling with parameter uncertainty and making predictions. In particular, I will highlight a seemingly universal "sloppy" pattern in parameter sensitivities and the implications of this pattern for developing parameter-rich models. In the second part of the talk, I will leverage such models to address an important question in evolutionary biology, to what extent is protein evolution constrained by protein function?