There has been a significant increase in cross-national and longitudinal data production in social science research in recent decades. Before drawing substantive conclusions based on cross-national and longitudinal survey data, researchers need to assess whether the constructs are measured in the same way across countries and time-points. If cross-national data are not tested for comparability, researchers risk confusing methodological artifacts as “real” substantive differences across countries. However, researchers often find it particularly difficult to establish the highest level of measurement invariance, that is, exact scalar invariance. When measurement invariance is rejected, it is crucial to understand why this was the case and to address its absence with approaches, such as alignment optimization or Bayesian structural equation modeling.