What structural and connectivity features of the human brain help to explain the extraordinary human cognitive abilities? We recently proposed a set of relevant connectomic fundamentals, some of which arise from the size scaling of the human brain relative to other primate brains, while others of these fundamentals may be uniquely human. In particular, we suggested that the remarkable increase of the size of the human brain due to its prolonged prenatal development has brought with it an increased sparsification, hierarchical modularization, as well as increased depth and cytoarchitectonic differentiation of brain networks. These characteristic features are complemented by a shift of projection origins to the upper layers of many cortical areas as well as the significantly prolonged postnatal development and plasticity of the upper cortical layers. Another fundamental aspect of cortical organization that has emerged in recent research is the alignment of diverse features of evolution, development, cytoarchitectonics, function, and plasticity along a principal, natural cortical axis from sensory (“outside”) to association (“inside”) areas. Here we highlight how this natural axis is integrated in the characteristic organization of the human brain. In particular, the human brain displays a developmental expansion of outside areas and a stretching of the natural axis such that outside areas are more widely separated from each other and from inside areas than in other species. We outline some functional implications of this characteristic arrangement. Author Summary Which brain connectivity features underlie the extraordinary human cognitive abilities? We have proposed a set of relevant connectomic fundamentals, including the increased sparsification, hierarchical modularization, as well as increased depth and cytoarchitectonic differentiation of cortical networks due to the prolonged prenatal development and size increase of the human brain. Such features are complemented by a shift of projection origins to the upper layers of many cortical areas and significantly prolonged postnatal development of such layers. Another fundamental aspect of cortical organization is the alignment of diverse features of evolution, development, cytoarchitectonics, function, and plasticity along a natural cortical axis from sensory (“outside”) to association (“inside”) areas. Here we highlight how this natural axis is integrated in the characteristic connectivity organization of the human brain.