The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set of methods. Promising goodness of fit methods are organized around three main categories: (1) checks on the extent to which test data fit model assumptions; (2) investigations of item and ability invariance; and (3) model-test data fit studies. Two current investigations of the researchers were also reviewed: the use of non-linear factor analysis to address the assumption of unidimensionality, and new methodologies for addressing questions of item invariance. The recommended strategy for assessing model-data fit is to accumulate a considerable amount of evidence that can be used to aid in the determination of the appropriateness of a particular use of an item response model. Since a researcher can not prove that a test measures a construct, it was concluded that the more evidence accumulated, the more informed the final decision will be about the use of an item response model. References, tables and figures are appended. (Author/PN)