In this dissertation, we present a design and implementation of a tool for automatic mapping and scheduling of large scientific application workflows onto distributed, heterogeneous Grid environments. The thesis of this work is that plan-ahead, application-independent scheduling of workflow applications based on performance models can reduce the turnaround time for Grid execution of the application, reducing burden of Grid application development. We applied the scheduling strategies successfully to Grid applications from the domains of bio-imaging and astronomy and demonstrated the effectiveness and efficiency of the scheduling approaches. We also proposed and evaluated a novel scheduling heuristic based on a middle-out traversal of the application workflow. A study showed that jobs have to wait in batch queues for a considerable amount of time before they begin execution. Schedulers must consider batch queue waiting times when scheduling Grid applications onto resources with batch queue front ends. Hence, we developed a smart scheduler that considers estimates of batch queue wait times when it constructs schedules for Grid applications. We compared the proposed scheduling techniques with existing dynamic scheduling strategies. An experimental evaluation of this scheduler on data-intensive workflows shows that its approach of planning schedules in advance improves over previous online scheduling approaches. We studied the scalability of the proposed scheduling approaches. To deal with the scale of future Grids consisting of hundreds of thousands of resources, we designed and implemented a novel cluster-level scheduling algorithm, which scales linearly on the number of abstract resource classes. An experimental evaluation using workflows from two applications shows that the cluster-level scheduler achieves good scalability without sacrificing the quality of schedule.