Recent years have witnessed both a growing number of cross-cultural datasets but also a growing awareness of problems connected with cross-cultural comparisons. In particular, researchers have realized that measurement invariance is a necessary precondition for a meaningful comparison of data across cultures or countries. The literature on measurement invariance is very rich and provides researchers with a variety of approaches which suggest when and how measurement invariance may be tested. This chapter provides an explanation of what measurement invariance is and offers a guide designed to help researchers interested in testing for measurement invariance. We distinguish six main issues that have to be addressed by researchers while testing for measurement invariance. The first issue concerns the level of measurement invariance to be tested (configural, metric or scalar), the second – the type of data used (continuous or ordinal-categorical), the third – choice of rules to evaluate whether measurement invariance is established, the fourth – decision about whether cross-loadings of the items are to be permitted, the fifth – the scope of measurement invariance (full or partial), and the sixth – the accuracy of invariance that needs to be established (i.e. exact or approximate). We describe possibilities to address these issues and formulate recommendations for applied researchers.