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Here we collected dense fMRI data in macaques and humans using the same movies, static-image sequences, and tasks, and developed a multivariate analysis method that aligns neural representations temporally and spatially. The resulting data-driven framework provides a quantitative translation of brain responses among individuals and between species. Using this framework, we uncovered a broadly conserved cross-species hierarchy of retinotopic visual areas and whole-brain correspondence. Yet within this structure, we found that higher-order macaque areas shared more information with lower-order human areas, particularly during movies, providing evidence of species differences. We also identified potential macaque precursors to human regions involved in high-level cognition, including theory-of-mind and reading. 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