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Examining factorial invariance provides the strongest test of the generalizability of psychological constructs across populations and should be investigated prior to cross-cultural interpretation of cognitive assessments. The aim of this systematic review was to critically evaluate the current evidence regarding the factorial invariance and the generalizability of cognition models across cultures. The review was structured using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The literature search identified 57 original studies examining the factorial invariance of cognitive ability assessments across cultures. The results were strongly supportive of the cross-cultural generalizability of the underlying cognitive model. Ten studies found configural invariance, 20 studies found weak or partial weak factorial invariance, 12 found strong or partial strong factorial invariance, and 13 found strict factorial invariance. However, the quality of the factorial invariance analyses varied between studies, with some analyses not adopting the hierarchical approach to factorial invariance analysis, leading to ambiguous results. No study that provided interpretable results in terms of the hierarchical approach to factorial invariance found a lack of factorial invariance. Overall, the results of this review suggest that i) the factor analytic models of cognitive abilities generalize across cultures, ii) the use of the hierarchical approach to factorial invariance is likely to find strong or strict factorial invariance, iii) the results are compatible with well-established Cattell-Horn-Carroll constructs being invariant across cultures. Future research into factorial invariance should follow the hierarchical analytic approach so as not to misestimate factorial invariance. Studies should also use the Cattell-Horn-Carroll taxonomy to systematize intelligence research.