Publisher Summary Cognitive diagnostic assessment traditionally has been performed through the use of specialized tests designed for this purpose. These tests are traditionally analyzed by straightforward statistical methods. However, within psychometrics, recently a much different picture of cognitive diagnosis has emerged in which statistical models are employed to obtain cognitive diagnosis information from conventional assessments not designed for cognitive diagnosis purposes. This chapter examines whether use of these statistical models accomplishes its purpose. The challenge to cognitive diagnostic models arises when a single test designed to measure a single proficiency is analyzed in an attempt to extract more information. Such design leads to a test relatively well described by the use of conventional univariate item response theory. To be sure, such an item response model does not provide a perfect description of the data, but the room for improvement appears to be modest. In addition, some causes of model variation are much more prosaic than the causes considered by cognitive diagnostic models.