This chapter examines methods of selecting models for high-dimensional tables. The model selection methods considered are the stepwise methods, e.g., forward selection and backward elimination, a modified backward elimination method from Aitkin (Journal of the Royal Statistical Society, Series B, 141, 195–223 (1978); Applied Statistics, 28, 233–242 (1979)) that controls the experimentwise error rate, and a backward elimination method from Wermuth (Biometrics, 32, 253–263 (1976)) that is restricted to decomposable models, see also Benedetti and Brown (Biometrics, 34, 680–686 (1978)). In addition, we discuss the use of the model selection criteria presented in Sect. 3.6 . Of course, it would be foolish to choose a model simply because some model selection procedure presents it to you as a good model. Other considerations such as model interpretability and the consistency of the data with model assumptions may dictate choosing some other model. It is always wise to use model selection methods to produce several apparently good models that can be investigated further. In line with this approach, the analysis of residuals and influential observations is also discussed in this chapter. Finally, the very act of model selection tends to arrive at models that fit unrealistically well, cf. Christensen (Plane answers to complex questions: The theory of linear models (5th edn.). Springer (2020), Section 14.2).