A fundamental but unsolved problem in neuroscience is how connections between neurons might underlie information processing in central circuits. Building wiring diagrams of neural networks may accelerate our understanding of how they compute. But even if we had wiring diagrams, it is critical to know what neurons in a circuit are doing: their physiology. In both the retina and cerebral cortex, a great deal is known about topographic specificity, such as lamination and cell-type specificity of connections. Little, however, is known about connections as they relate to function. Here, we review how advances in functional imaging and electron microscopy have recently allowed the examination of relationships between sensory physiology and synaptic connections in cortical and retinal circuits.