The measurement of cognitive abilities across diverse cultural, racial, and ethnic groups has a contentious history, with broad political, legal, economic, and ethical repercussions. Advances in psychometric methods and converging scientific ideas about genetic variation afford new tools and theoretical contexts to move beyond the reflective analysis of between-group test score discrepancies. Neuropsychology is poised to benefit from these advances to cultivate a richer understanding of the factors that underlie cognitive test score disparities. To this end, the present article considers several topics relevant to the measurement of cognitive abilities across groups from diverse ancestral origins, including fairness and bias, equivalence, diagnostic validity, item response theory, and differential item functioning.