Abstract: The physical and mathematical study of complex systems facilitates critical insights into real-world phenomena. While a plethora of theoretical and analytical tools are available to support this study, my particular focus has been on recent developments in statistical mechanics and network theory that together provide a principled framework in which to characterize the organization of systems composed of many interacting parts. At the interdisciplinary boundary between statistical physics, applied mathematics, and neuroscience, I study the human brain as a model system. Here, a combination of mathematical modeling and time series analysis enables the prediction of system behavior, facilitating a direct feedback loop between theory and experiment. Specifically, I examine structural and functional brain networks using data from non-invasive neuroimaging techniques. Through the principled characterization of this system, we can begin to determine fundamental organizational principles of both underlying structure and functional dynamics. In addition to understanding phenomena specific to the brain system, these studies facilitate the examination of more general questions related to the relationships between system organization – both static and dynamic – and performance, as well as the influence of external constraints (e.g., energetic or spatial) on that organization. Resultant insights can be transferred to systems as varied as social collectives, granular materials, and gene regulation.