This chapter introduces the use of confirmatory factor analysis (CFA) and item response theory (IRT) modeling, particularly as each is used to evaluate measurement invariance of assessment devices. It covers CFA, which is a special case of the common factor model. The chapter discusses basic ideas with regard to model specification and evaluation. It explains how measurement invariance is pursued in CFA models. The chapter also discusses the parallel issues with regard to IRT models, including both basic forms of IRT model and the study of measurement invariance within such models. It provides illustrations of analyses with empirical data to demonstrate how to fit such models and evaluate results. While good introductory presentations are available for both CFA and IRT, the authors look forward to the increased use of the two techniques for investigating measurement invariance and improving the nature of measurements used in psychological sciences.