Recent advances in mapping cortical areas in the human brain provide a basis for investigating the significance of their spatial arrangement. Here we describe a dominant gradient in cortical features that spans between sensorimotor and transmodal areas. We propose that this gradient constitutes a core organizing axis of the human cerebral cortex, and describe an intrinsic coordinate system on its basis. Studying the cortex with respect to these intrinsic dimensions can inform our understanding of how the spectrum of cortical function emerges from structural constraints. Advances in neuroimaging technologies and analytics have enabled the discovery of gradients in microstructure, connectivity, gene expression, and function in the human cerebral cortex. The notion that functional processing hierarchies are confined to sensorimotor systems is challenged by recent descriptions of global hierarchies, extending throughout transmodal association areas. An innovative line of research has uncovered a cortical hierarchy in the temporal domain that accounts for spatially distributed functional specialization.