Bayesian approaches to learning problems have many virtues, including their ability to make use of prior knowledge and their ability to link related sources of information, but they also have many vices, notably the strong parametric assumptions that are often invoked willy-nilly in practical Bayesian modeling. Nonparametric Bayesian methods offer a way to make use of the Bayesian calculus without the parametric handcuffs. In this talk I describe several recent explorations in nonparametric Bayesian modeling and inference, including various versions of "Chinese restaurant process priors" that allow flexible structures to be learned and allow sharing of statistical strength among sets of related structures. I discuss applications to problems in bioinformatics and information retrieval.