Person-fit methods based on classical test theory-and item response theory (IRT), and methods investigating particular types of response behavior on tests, are examined. Similarities and differences among person-fit methods and their advantages and disadvantages are discussed. Sound person-fit methods have been derived for the Rasch model. For other IRT models, the empirical and theoretical distributions differ for most person-fit statistics when used with short and moderate length tests. The detection rate of person-fit statistics depends on the type of misfitting item-score patterns, test length, and trait levels. The usefulness of person-fit statistics for improving measurement depends on the application.