Aiming at aggregating numerous distributed resources to provide immense computing power, Grid computing has emerged as a promising paradigm to run complex composite applications such as workflows. However, the inherent uncertainties of grid systems as well as the structural complexity of workflow applications make it extremely challenging to schedule workflows in an efficient way, regardless of whether the objective is to minimize execution time or meet specific user and/or system Quality of Service (QoS) requirements. For both these cases, this thesis considers scheduling problems motivated by grid uncertainties and advances the state-of-the-art by developing new techniques to address these problems.First, based on existing scheduling heuristics, a Monte-Carlo approach is developed to minimize the average makespan (i.e., the overall execution time) in the presence of task estimates exhibiting limited uncertainty in the form of (controlled) random behaviour. Next, a scenario where performance prediction is difficult to obtain and resource availability may vary over time, is considered. A low-cost efficient just-in-time heuristic is proposed to cope with grid uncertainties.After addressing these performance-driven scheduling problems, a QoS-driven problem, which considers not only the aforementioned uncertainties but also the uncertainty caused by queue-based scheduling, is examined. In order to tackle all these uncertainties, an integrated scheduling model consisting of three supportive techniques is developed. Extensive evaluation using simulation shows that the proposed techniques can achieve substantial improvements towards the ultimate goal of providing a good solution for QoS-driven workflow scheduling on the Grid.