Hierarchy is a major organizational principle of the cortex and underscores modern computational theories of cortical function. Consideration of the role of the local microcircuit in the amplification of inputs, leads to the argument that distance dependent changes in the laminar profiles of connectivity constitute the structural signatures of hierarchy. Statistical modeling of these signatures 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 Exploring the laminar basis of inter-areal interactions, we suggest, can be achieved with concerted experiments capitalizing on recent technical advances in tract-tracing, high-resolution fMRI, optogenetics and mathematical modeling thereby allowing a much improved understanding of the computational properties of the cortex. However, because inter-areal interactions involve cortical layers that have been the target of important evolutionary changes in the primate and human lineage, their investigation will need to include interspecies comparisons.