Growing access to large-scale longitudinal structural neuroimaging data has fundamentally altered our understanding of cortical development en route to human adulthood, with consequences for basic science, medicine, and public policy. In striking contrast, basic anatomical development of subcortical structures such as the striatum, pallidum, and thalamus has remained poorly described--despite these evolutionarily ancient structures being both intimate working partners of the cortical sheet and critical to diverse developmentally emergent skills and disorders. Here, to begin addressing this disparity, we apply methods for the measurement of subcortical volume and shape to 1,171 longitudinally acquired structural magnetic resonance imaging brain scans from 618 typically developing males and females aged 5-25 y. We show that the striatum, pallidum, and thalamus each follow curvilinear trajectories of volume change, which, for the striatum and thalamus, peak after cortical volume has already begun to decline and show a relative delay in males. Four-dimensional mapping of subcortical shape reveals that (i) striatal, pallidal, and thalamic domains linked to specific fronto-parietal association cortices contract with age whereas other subcortical territories expand, and (ii) each structure harbors hotspots of sexually dimorphic change over adolescence--with relevance for sex-biased mental disorders emerging in youth. By establishing the developmental dynamism, spatial heterochonicity, and sexual dimorphism of human subcortical maturation, these data bring our spatiotemporal understanding of subcortical development closer to that of the cortex--allowing evolutionary, basic, and clinical neuroscience to be conducted within a more comprehensive developmental framework.