Although multi-group comparisons have been of substantial interest to cross-cultural psychologists for the past 6 decades, the critical importance of measurement invariance was neither recognized nor made possible until the seminal CFA work of Jöreskog (1971) in developing a method capable of such analyses. Further complications have been the assumption that any difference findings derive from the cultures involved, albeit with no identification or justification for such differences (Matsumoto & Yoo, 2006). Indeed, the 1990’s saw a substantial increase in testing for measurement and latent mean equivalencies across numerous groups that commonly included countries. It was during this 20-year period (1990-2010) that the impracticality of the CFA approach to these analyses became known and the development of a new generation of alternative methodological procedures that allow for approximate, rather than exact measurement invariance across groups became known. In this chapter, we trace the early difficulties in testing for measurement equivalence across cultural groups, identify common quandaries encountered in applying these analyses across multiple groups, and outline the pros and cons pertinent to the more recent statistical procedures used in testing for approximate measurement equivalence.