Hierarchy is a major organizational principle of the cortex and underscores modern computational theories of cortical function. The local microcircuit amplifies long-distance inter-areal input, which show distance-dependent changes in their laminar profiles. Statistical modeling of these changes in laminar profiles demonstrates that inputs from multiple hierarchical levels to their target areas show remarkable consistency, allowing the construction of a cortical hierarchy based on a principle of hierarchical distance. The statistical modeling that is applied to structure can also be applied to laminar differences in the oscillatory coherence between areas thereby determining a functional hierarchy of the cortex. Close examination of the anatomy of inter-areal connectivity reveals a dual counterstream architecture with well-defined distance-dependent feedback and feedforward pathways in both the supra- and infragranular layers, suggesting a multiplicity of feedback pathways with well-defined functional properties. These findings are consistent with feedback connections providing a generative network involved in a wide range of cognitive functions. A dynamical model constrained by connectivity data shed insights into the experimentally observed signatures of frequency-dependent Granger causality for feedforward versus feedback signaling. Concerted experiments capitalizing on recent technical advances and combining tract-tracing, high-resolution fMRI, optogenetics and mathematical modeling hold the promise of a much improved understanding of lamina-constrained mechanisms of neural computation and cognition. However, because inter-areal interactions involve cortical layers that have been the target of important evolutionary changes in the primate lineage, these investigations will need to include human and non-human primates comparisons.