This Perspective considers the influential notion of a canonical (cortical) microcircuit in light of recent theories about neuronal processing. Specifically, we conciliate quantitative studies of microcircuitry and the functional logic of neuronal computations. We revisit the established idea that message passing among hierarchical cortical areas implements a form of Bayesian inference-paying careful attention to the implications for intrinsic connections among neuronal populations. By deriving canonical forms for these computations, one can associate specific neuronal populations with specific computational roles. This analysis discloses a remarkable correspondence between the microcircuitry of the cortical column and the connectivity implied by predictive coding. Furthermore, it provides some intuitive insights into the functional asymmetries between feedforward and feedback connections and the characteristic frequencies over which they operate.