Publisher Summary This chapter outlines the ways Grid technologies are being used in computational astrophysics today and the ways these technologies will be used in the future. Although it focuses on the needs and applications of the numerical relativity community, the tools and experiences described are quite general and apply to many other computational science disciplines. Computational astrophysicists have different requirements for the Grid according to whether they develop or run codes. Those developing Grid-enabled codes need tools and procedures for diagnosing and solving the problems that arise in this complex environment, whereas those running codes are more interested in reliability, ease of use, and new functionality such as remote techniques for interaction and collaboration. All of the scenarios related to the use of Grid technologies in computational astrophysics are motivated by the needs of present-day astrophysicists, are working now in prototype form, and have been tested on real codes and in real production environments using today's Grid technologies. The best way to bring these scenarios into everyday production use is to develop Grid applications in close collaboration with Grid infrastructure developers. Such a partnership ensures that application requirements found by prototyping and testing scenarios are addressed and solved and that the applications are ready to exploit the Grid as soon as possible.