How do the laminar circuits of visual cortical areas V1 and V2 implement context-sensitive binding processes such as perceptual grouping and attention, and how do these circuits develop and learn in a stable way? Recent neural models clarify how preattentive and attentive perceptual mechanisms are intimately linked within the laminar circuits of visual cortex, notably how bottom-up, top-down, and horizontal cortical connections interact within the cortical layers. These laminar circuits allow the responses of visual cortical neurons to be influenced, not only by the stimuli within their classical receptive fields, but also by stimuli in the extra-classical surround. Such context-sensitive visual processing can greatly enhance the analysis of visual scenes, especially those containing targets that are low contrast, partially occluded, or crowded by distractors. Attentional enhancement can selectively propagate along groupings of both real and illusory contours, thereby showing how attention can selectively enhance object representations. Recent models explain how attention may have a stronger facilitatory effect on low contrast than on high contrast stimuli, and how pop-out from orientation contrast may occur. The specific functional roles which the model proposes for the cortical layers allow several testable neurophysiological predictions to be made. Model mechanisms clarify how intracortical and intercortical feedback help to stabilize cortical development and learning. Although feedback plays a key role, fast feedforward processing is possible in response to unambiguous information. Model circuits are capable of synchronizing quickly, but context-sensitive persistence of previous events can influence how synchrony develops.