This talk will discuss Bayesian methods of inference and develop flexible models for financial applications. One approach to flexible modeling is Bayesian nonparametric methods which use an infinite mixture model. A Dirichlet process mixture and an infinite hidden Markov model, a time-dependent version of the former, will be reviewed. Another important feature of financial data is heteroskedasticity. A popular class of specifications for the evolution of the conditional covariance of asset returns is the multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) model. We will discuss an approach to combine an infinite mixture model with MGARCH dynamics suitable to capture the complex distribution of financial data. The talk will conclude with applications of these models to portfolio choice problems to evaluate their usefulness.