Major neuropsychiatric disorders such as psychosis are increasingly acknowledged to be disorders of brain connectivity. Yet, tools to map, model, predict, and change connectivity are difficult to develop, largely due to the complex, dynamic, and multivariate nature of interactions between brain regions. Network neuroscience provides a theoretical framework and mathematical toolset to address these difficulties. Building on areas of mathematics such as graph theory, network neuroscience in its simplest form summarizes neuroimaging data by treating brain regions as nodes in a graph, and by treating interactions or connections between nodes as edges in the graph. Network metrics can then be used to quantitatively describe the architecture of the graph, which in turn reflects the network’s function. Here we review evidence supporting the utility of network neuroscience in understanding psychiatric disorders, with a particular focus on normative brain network development and abnormalities associated with psychosis. We also emphasize relevant methodological challenges such as motion artifact correction, which are particularly important to consider when applying network tools to developmental neuroimaging data. We close with a discussion of several emerging frontiers of network neuroscience in psychiatry, including generative network modeling and network control theory. We aim to offer an accessible introduction to this emerging field, and motivate further work that uses network neuroscience to better understand the normative development of brain networks, and alterations in that development that accompany or foreshadow psychiatric disease.