The term “Grid Computing” refers to the use, for computational purposes, of emerging distributed Grid infrastructures: that is, network and middleware services designed to provide on-demand and high-performance access to all important computational resources within an organization or community. Grid computing promises to enable both evolutionary and revolutionary changes in the practice of computational science and engineering based on new application modalities such as high-speed distributed analysis of large datasets, collaborative engineering and visualization, desktop access to computation via “science portals,” rapid parameter studies and Monte Carlo simulations that use all available resources within an organization, and online analysis of data from scientific instruments. In this article, I examine the status of Grid computing circa 2000, briefly reviewing some relevant history, outlining major current Grid research and development activities, and pointing out likely directions for future work. I also present a number of case studies, selected to illustrate the potential of Grid computing in various areas of science. © 2001 American Institute of Physics.