Grid computing has emerged as a global cyber-infrastructure for the next-generation of e-Science applications by integrating large-scale, distributed and heterogeneous resources. Scientific communities are utilizing Grids to share, manage and process large data sets. In order to support complex scientific experiments, distributed resources such as computational devices, data, applications, and scientific instruments need to be orchestrated while managing the application workflow operations within Grid environments. This thesis investigates properties of Grid workflow management systems, presents a workflow engine and algorithms for mapping scientific workflow applications to Grid resources based on specified QoS (Quality of Service) constraints. (For complete abstract open document)