Abstract: Recent advances in network science have greatly increased our understanding of the structure and function of many networked systems, ranging from transportation networks, to social networks, the internet, ecosystems, and biochemical and gene transcription pathways. Network approaches are also increasingly applied to the brain, at several levels of scale from cells to entire nervous systems. Early studies in this emerging field of brain connectomics have focused on mapping brain network topology and identifying some of its characteristic features, including small world attributes, modularity and hubs. More recently, the emphasis has shifted towards linking brain network topology to brain dynamics, the patterns of functional interactions that emerge from spontaneous and evoked neuronal activity. I will give an overview of recent work characterizing the structure of complex brain networks, with particular emphasis on studies demonstrating how the network topology of the connectome constrains and shapes its capacity to process and integrate information.