As the practice of science moves beyond the single investigator due to the complexity of the problems that now dominate science, large collaborative and multi-institutional teams are needed to address these problems. In order to support this shift in science, the computing and data-handling infrastructure that is essential to most of modern science must also change in order to support this increased complexity. This is the goal of computing and data Grids: software infrastructure that facilitates solving large-scale problems by providing the mechanisms to access, aggregate, and manage the computer network-based infrastructure of science. This infrastructure includes computing systems, data archive systems, scientific instruments, and computer-mediated human collaborations. This paper examines several large-scale science problems, their requirements for computing and data Grid infrastructure, and the current approaches to providing the necessary functionality.