Deep convolutional neural networks (DCNNs) trained for face identification can rival and even exceed human-level performance. The ways in which the internal face representations in DCNNs relate to human cognitive representations and brain activity are not well understood. Nearly all previous studies focused on static face image processing with rapid display times and ignored the processing of naturalistic, dynamic information. To address this gap, we developed the largest naturalistic dynamic face stimulus set in human neuroimaging research (700+ naturalistic video clips of unfamiliar faces). We used this naturalistic dataset to compare representational geometries estimated from DCNNs, behavioral responses, and brain responses. We found that DCNN representational geometries were consistent across architectures, cognitive representational geometries were consistent across raters in a behavioral arrangement task, and neural representational geometries in face areas were consistent across brains. Representational geometries in late, fully connected DCNN layers, which are optimized for individuation, were much more weakly correlated with cognitive and neural geometries than were geometries in late-intermediate layers. The late-intermediate face-DCNN layers successfully matched cognitive representational geometries, as measured with a behavioral arrangement task that primarily reflected categorical attributes, and correlated with neural representational geometries in known face-selective topographies. Our study suggests that current DCNNs successfully capture neural cognitive processes for categorical attributes of faces but less accurately capture individuation and dynamic features.