Determining whether people in certain countries score differently in measurements of interest or whether concepts relate differently to each other across nations can indisputably assist in testing theories and advancing our sociological knowledge. However, meaningful comparisons of means or relationships between constructs within and across nations require equivalent measurements of these constructs. This is especially true for subjective attributes such as values, attitudes, opinions, or behavior. In this review, we first discuss the concept of cross-group measurement equivalence, look at possible sources of nonequivalence, and suggest ways to prevent it. Next, we examine the social science methodological literature for ways to empirically test for measurement equivalence. Finally, we consider what may be done when equivalence is not supported by the data and conclude with a review of recent developments that offer exciting directions and solutions for future research in cross-national measurement equivalence assessment.