Hemispheric asymmetries are a central principle of nervous system architecture and shape the functional organization of most cognitive systems. Structural gray matter asymmetries and callosal interactions have been identified as contributing neural factors but always fell short to constitute a full explanans. Meanwhile, recent advances in in vivo white matter tractography have unrevealed the asymmetrical organization of many intrahemispheric white matter pathways, which might serve as the missing link to explain the substrate of functional lateralization. By taking into account callosal interactions, gray matter asymmetries and asymmetrical interhemispheric pathways, we opt for a new triadic model that has the potential to explain many observations which cannot be elucidated within the current frameworks of lateralized cognition.