Fifty years ago, John von Neumann compared the architecture of the brain with that of the computers he invented and which are still in use today. In those days, the organization of computers was based on concepts of brain organization. Here, we give an update on current results on the global organization of neural systems. For neural systems, we outline how the spatial and topological architecture of neuronal and cortical networks facilitates robustness against failures, fast processing and balanced network activation. Finally, we discuss mechanisms of self-organization for such architectures. After all, the organization of the brain might again inspire computer architecture.