Examples of the impact of statistical theory on assessment practice are provided from the perspective of a statistician trained in theoretical statistics who began to work on assessments. Goodness of fit of item-response models is examined in terms of restricted likelihood-ratio tests and generalized residuals. Minimum discriminant information adjustment is used for linking with no anchors or problematic anchors and for repeater analysis. Assessment issues are examined in cases in which the number of parameters is large relative to the number of observations.