Over the last few years, several nations around the world have set up Grids to share resources such as computers, data, and instruments to enable collaborative science, engineering, and business applications. These Grids follow a restricted organizational model wherein a Virtual Organization (VO) is created for a specific collaboration and all interactions such as resource sharing are limited to within the VO. Therefore, dispersed Grid initiatives have led to the creation of disparate Grids with little or no interaction between them. In this paper, we propose a model that: (a) promotes interlinking of islands of Grids through peering arrangements to enable InterGrid resource sharing; (b) provides a scalable structure for Grids that allow them to interconnect with one another and grow in a sustainable way; (c) creates a global Cyberinfrastructure to support e-Science and e-Business applications. This work identifies and proposes architecture, mechanisms, and policies that allow the internetworking of Grids and allows Grids to grow in a similar manner as the Internet. We term the structure resulting from such internetworking between Grids as the InterGrid. The proposed InterGrid architecture is composed of InterGrid Gateways responsible for managing peering arrangements between Grids. We discuss the main components of the architecture and present a research agenda to enable the InterGrid vision.