Recent breakthroughs (some achieved in the MoA (Matters of Activity) project) in comparative neurobiological research highlight specific features of the connectivity structure of the human brain, which open new perspectives on understanding the neural mechanisms of human-specific higher cognition and language. In delineating the material basis of human cognition and language, neurobiologically founded modelling appears as the method of choice, as it allows not only for ‘external fitting’ of models to key experimental data, but, in addition, for ‘internal’ or ‘material fitting’ of the model components to the structure of brains, cortical areas and neuronal circuits.