Inferring hidden structure from noisy observations is a problem addressed by Bayesian statistical learning, which aims to identify optimal models of the process that generated the observations given assumptions that constrain the space of potential solutions. Animals and machines face similar "model-selection" problems to infer latent properties and predict future states of the world. Here we review recent attempts to explain how intelligent agents address these challenges and how their solutions relate to Bayesian principles. We focus on how constraints on available information and resources affect inference and propose a general framework that uses benefit(accuracy) and accuracy(cost) curves to assess optimality under these constraints.