Simple resource specification, resource selection, and effective binding are critical capabilities for Grid middleware. We describe the Virtual Grid, an abstraction for providing these capabilities complex resource environments. Elements of the Virtual Grid include a novel resource description language (vgDL) and a resource selection and binding component (vgFAB), which accepts a vgDL specification and returns a Virtual Grid, that is, a set of selected and bound resources. The goals of vgFAB are efficiency, scalability, robustness to high resource contention, and the ability to produce results with quantifiable high quality. We present the design of vgDL, showing how it captures application-level resource abstractions using resource aggregates and connectivity amongst them. We present and evaluate a prototype implementation of vgFAB. Our results show that resource selection and binding for virtual grids of 10,000's of resources can scale up to grids with millions of resources, identifying good matches in less than one second. Further, these matches have quantifiable quality, enabling applications to have high confidence in the results. We demonstrate the effectiveness of our combined selection and binding approach in the presence of resource contention, showing that robust selection and binding can be achieved at moderate cost.