This chapter provides a brief account of model selection in hidden Markov models (HMM), and describes the use of pseudo-residuals in order to check for deficiencies in the selected model. It outlines the most popular approaches to model selection. The analysis of the pseudo-residuals of an HMM serves two purposes: the assessment of the general fit of a selected model, and the detection of outliers. The normal version of pseudo-residuals has the advantage that the absolute value of the residual increases with increasing deviation from the median and that extreme observations can be identified more easily on a normal scale. The Bayesian approach to model selection is to select the family which is estimated to be most likely to be true. In the frequentist approach one selects the family estimated to be closest to the operating model.