The human brain is a complex network. An important first step toward understanding the function of such a network is to map its elements and connections, to create a comprehensive structural description of the network architecture. This paper reviews current empirical efforts toward generating a network map of the human brain, the human connectome, and explores how the connectome can provide new insights into the organization of the brain's structural connections and their role in shaping functional dynamics. Network studies of structural connectivity obtained from noninvasive neuroimaging have revealed a number of highly nonrandom network attributes, including high clustering and modularity combined with high efficiency and short path length. The combination of these attributes simultaneously promotes high specialization and high integration within a modular small‐world architecture. Structural and functional networks share some of the same characteristics, although their relationship is complex and nonlinear. Future studies of the human connectome will greatly expand our knowledge of network topology and dynamics in the healthy, developing, aging, and diseased brain.