Imaging connectomics based on graph theory has become an effective and unique methodological framework for studying structural and functional connectivity patterns of the developing brain. Normal brain development is characterized by continuous and significant network evolution throughout infancy, childhood, and adolescence, following specific maturational patterns. Disruption of these normal changes is associated with neuropsychiatric developmental disorders, such as autism spectrum disorders or attention-deficit hyperactivity disorder. In this review, we focused on the recent progresses regarding typical and atypical development of human brain networks from birth to early adulthood, using a connectomic approach. Specifically, by the time of birth, structural networks already exhibit adult-like organization, with global efficient small-world and modular structures, as well as hub regions and rich-clubs acting as communication backbones. During development, the structure networks are fine-tuned, with increased global integration and robustness and decreased local segregation, as well as the strengthening of the hubs. In parallel, functional networks undergo more dramatic changes during maturation, with both increased integration and segregation during development, as brain hubs shift from primary regions to high order functioning regions, and the organization of modules transitions from a local anatomical emphasis to a more distributed architecture. These findings suggest that structural networks develop earlier than functional networks; meanwhile functional networks demonstrate more dramatic maturational changes with the evolution of structural networks serving as the anatomical backbone. In this review, we also highlighted topologically disorganized characteristics in structural and functional brain networks in several major developmental neuropsychiatric disorders (e.g., autism spectrum disorders, attention-deficit hyperactivity disorder and developmental dyslexia). Collectively, we showed that delineation of the brain network from a connectomics perspective offers a unique and refreshing view of both normal development and neuropsychiatric disorders.