This chapter provides an overview of posterior-based specification testing methods and model selection criteria that have been developed in recent years. For the specification testing methods, the first method is the posterior-based version of IOSA test. The second method is motivated by the power enhancement technique. For the model selection criteria, we first review the deviance information criterion (DIC). We discuss its asymptotic justification and shed light on the circumstances in which DIC fails to work. One practically relevant circumstance is when there are latent variables that are treated as parameters. Another important circumstance is when the candidate model is misspecified. We then review DICL for latent variable models and DICM for misspecified models.