Mixtures of Polya trees models are straightforward to code and provide a highly flexible alternative when a parametric model may only hold approximately. In this talk, I provide computational strategies for obtaining semiparametric inference for mixtures of finite Polya trees models given a standard parameterization, including models that would be difficult to fit using Dirichlet process mixtures. Recommendations are put forth on choosing the level of a finite Polya tree and model comparison is discussed. Several examples demonstrate the utility of Polya tree modeling including data on bivariate (CD4,CD8) counts fit to a semiparametric linear mixed model; the classic V.A. lung cancer study data fit to proportional hazards, proportional odds, and accelerated failure time models; and serology scores modeled with a stochastic order constraint.