At rest, human brain functional networks display striking modular architecture in which coherent clusters of brain regions are activated. The modular account of brain function is pervasive, reliable, and reproducible. Yet, a complementary perspective posits a core–periphery or rich-club account of brain function, where hubs are densely interconnected with one another, allowing for integrative processing. Unifying these two perspectives has remained difficult due to the fact that the methodological tools to identify modules are entirely distinct from the methodological tools to identify core–periphery structure. Here, we leverage a recently-developed model-based approach—the weighted stochastic block model—that simultaneously uncovers modular and core–periphery structure, and we apply it to functional magnetic resonance imaging data acquired at rest in 872 youth of the Philadelphia Neurodevelopmental Cohort. We demonstrate that functional brain networks display rich mesoscale organization beyond that sought by modularity maximization techniques. Moreover, we show that this mesoscale organization changes appreciably over the course of neurodevelopment, and that individual differences in this organization predict individual differences in cognition more accurately than module organization alone. Broadly, our study provides a unified assessment of modular and core–periphery structure in functional brain networks, offering novel insights into their development and implications for behavior.