Our modern ability to acquire and generate huge amounts of data can potentially enable rapid progress in science and engineering, but we may not live up to that promise if our ability to create data outstrips our ability to make sense of that data. Visual computing tools are essential to gain insights into data by combining computational and statistical analysis with the power of the human perceptual and cognitive system and enabling data exploration through interactive visualizations. In this talk I will present our work on visual computing in Connectomics, a new field in neuroscience that aims to apply biology and computer science to the grand challenge of determining the detailed neural circuitry of the brain. I will give an overview of the computational challenges and describe visual computing approaches that we developed to discover and analyze the brain's neural network. The key to our methods is to keep the user in the loop, either for providing input to our fully-automatic reconstruction methods, or for validation and corrections of the reconstructed neural structures. The main challenges we face are how to analyze petabytes of image data in an efficient and scalable way, how to automatically reconstruct very large and dense neural circuits from nanoscale-resolution electron micrographs, and how to analyze the brain's neural network once we have discovered it.