Neuronal circuits of the cerebral cortex are the structural basis of mammalian cognition. The same qualitative components and connectivity motifs are repeated across functionally specialized cortical areas and mammalian species, suggesting a single underlying algorithmic motif. Here, we propose a perspective on current knowledge of the cortical structure, from which we extract two core principles for computational modeling. The first principle is that cortical cell types fulfill distinct computational roles. The second principle is that cortical connectivity can be efficiently characterized by only a few canonical blueprints of connectivity between cell types. Starting with these two foundational principles, we outline a general framework for building functional and mechanistic models of cortical circuits.