Nonparametric Bayesian methods provide flexible and highly adaptable approaches for biomedical data analysis. In this talk, I discuss the use of nonparametric Bayesian methods in tumor subclone inference and missing data modeling. (1) Tumor subclone reconstruction from next-generation sequencing data is a major challenge in computational biology. I present a Bayesian feature allocation model for such reconstruction, using the categorical Indian buffet process as a prior model for subclones. To recover the phylogenetic relationship of subclones, I then propose a dependent feature allocation model, where the dependence is introduced through a tree structure. A key innovation in my method is the use of short reads mapped to pairs of proximal single nucleotide variants, known as mutation pairs. (2) Missing data are common in longitudinal studies due to subject dropout. I develop a nonparametric Bayesian approach to non-ignorable missing data via Gaussian process priors and Bayesian additive regression trees. My method allows for incorporating information from auxiliary covariates and is able to capture complex structures among the response, missingness and auxiliary covariates.