With the advent of Grid and application technologies, scientists and engineers are building more and more complex applications to manage and process large data sets, and execute scientific experiments on distributed resources. Such application scenarios require means for composing and executing complex workflows. Therefore, many efforts have been made towards the development of workflow management systems for Grid computing. In this paper, we propose a taxonomy that characterizes and classifies various approaches for building and executing workflows on Grids. We also survey several representative Grid workflow systems developed by various projects world-wide to demonstrate the comprehensiveness of the taxonomy. The taxonomy with survey not only highlights the state-of-the-art in Grid workflow systems, but also outlines the needs of further enhancements.