How rich functionality emerges from the invariant structural architecture of the brain remains a major mystery in neuroscience. Recent applications of network theory and theoretical neuroscience to large-scale brain networks have started to dissolve this mystery. Network analyses suggest that hierarchical modular brain networks are particularly suited to facilitate local (segregated) neuronal operations and the global integration of segregated functions. Although functional networks are constrained by structural connections, context-sensitive integration during cognition tasks necessarily entails a divergence between structural and functional networks. This degenerate (many-to-one) function-structure mapping is crucial for understanding the nature of brain networks. The emergence of dynamic functional networks from static structural connections calls for a formal (computational) approach to neuronal information processing that may resolve this dialectic between structure and function.