The past and current views of language evolution all center around a crucial question: What led to the human faculty of language and can it be explained by continuity of phylogenesis from non-human to human primates? The view that is presented here holds that the difference between human and non-human primates lies in the structure of their brains, particularly in the way the relevant brain areas are connected by white matter fiber tracts. During the evolution of language two crucial abilities had to evolve: these are first, sensory-motor learning, and second, the ability to process hierarchical structures. Across-species comparisons between the human and non-human primate brain reveal cytoarchitectonic and connectivity differences. Although still under discussion, the available paleoanthropological findings suggest a reorganization of the brain during phylogeny, and a possible rewiring which, due to the prolonged ontogeny in humans, is shaped by environmental input.