BACKGROUND: Reviewed in this article are issues relating to the study of invariance and differential item functioning (DIF). The aim of factor analyses and DIF, in the context of invariance testing, is the examination of group differences in item response conditional on an estimate of disability. Discussed are parameters and statistics that are not invariant and cannot be compared validly in crosscultural studies with varying distributions of disability in contrast to those that can be compared (if the model assumptions are met) because they are produced by models such as linear and nonlinear regression. OBJECTIVES: The purpose of this overview is to provide an integrated approach to the quantitative methods used in this special issue to examine measurement equivalence. The methods include classical test theory (CTT), factor analytic, and parametric and nonparametric approaches to DIF detection. Also included in the quantitative section is a discussion of item banking and computerized adaptive testing (CAT). METHODS: Factorial invariance and the articles discussing this topic are introduced. A brief overview of the DIF methods presented in the quantitative section of the special issue is provided together with a discussion of ways in which DIF analyses and examination of invariance using factor models may be complementary. CONCLUSIONS: Although factor analytic and DIF detection methods share features, they provide unique information and can be viewed as complementary in informing about measurement equivalence.