Mixtures of Polya trees (MPT) naturally generalize parametric families of distributions such as the normal, Weibull, etc. by adding additional parameters in the form of conditional probabilities. This flexible class of nonparametric prior densities is formally introduced, including simple examples, and various desirable properties are discussed. This introduction is followed by two quite different applications of MPT modeling. The first is a so-called "density regression" model in which the entire shape of a density changes smoothly with regressors, useful in growth curve modeling and non-exchangeable random effects in GLMMs. The model likelihood factors into the product of several logistic regression likelihoods, making inference feasible even for very large sample sizes. In the second application, the MPT forms the basis of a "black box" MCMC sampler. The MPT approximation to an unnormalized density, such as a posterior, is iteratively built using a simple, fast algorithm that operates like an archaeological dig. The MPT approximation is then used as an independence proposal. This simple method works surprisingly well across test cases and real data models.