•Addresses three key theoretical issues in research on cultural intelligence (CQ).•Each factor in the CQ bi-factor model provides unique and holistic information.•CQ factors have differential relationships with intercultural effectiveness.•Cultural decision making and adjustment mediate relationships with task performance.•Addresses moderated CQ relationships. Today’s pervasiveness of intercultural interactions has spawned scholarly interest in cultural intelligence (CQ) – the capability to function effectively across cultures. Applying meta-analytic techniques, we harness the recent explosion of research on the four-factor model of CQ to address three fundamental, yet unresolved theoretical issues. First, we explicate the benefits of conceptualizing and modeling CQ as a bi-factor model where each factor provides both unique and holistic information. Results shed light on Gelfand’s puzzle of whether to facet or not and clearly show the value of the four factors. Second, we advance and test a theoretical model delineating differential relationships between the four CQ factors and three forms of intercultural effectiveness. Findings, based on 199 independent samples (N = 44,155), underscore the value of a nuanced, theoretical model of CQ with differential effects of the four factors. Finally, going beyond prior research, we also address mediated and moderated relationships and expand our understanding of the CQ nomological network. We discuss the implications of these findings for theorizing about the CQ factors and suggest directions for future research.