In the previous chapter, item response theory (IRT)models for dichotomously scored items were illustrated. However, it is very common that psychological and educational tests are characterized by polytomous items to supply a more precise piece of information about the response process. The most relevant case, to which we will typically refer, concerns items with ordered categories. In this context, it is necessary to provide a suitable generalization of the models for binary data to account for the categorical nature of the item responses.