The visual cortex performs some of the first, fundamental tasks in the dynamical processing of visual information by the brain. It also has a fascinating neuronal architecture that is characterized by a laminar structure, activity and coupling across multiple scales, and an input signal that is apparently a mix of ordered and disordered information. The functional consequences of this architecture are just beginning to be understood. I will discuss coarse-graining (CG), or homogenization, methods used for constructing reduced models of the neuronal network dynamics. The resulting CG models capture both the effects of ordered and disordered input, and of cortical network coupling, and are being used to understand the mechanisms by which more complicated "point-neuron" models produce physiologically consistent responses.