Grids offer a transparent interface to geographically scattered computation, communication, storage and other resources. In this chapter we propose and evaluate QoS-aware and fair scheduling algorithms for Grid Networks, which are capable of optimally or near-optimally assigning tasks to resources, while taking into consideration the task characteristics and QoS requirements. We categorize Grid tasks according to whether or not they demand hard performance guarantees. Tasks with one or more hard requirements are referred to as Guaranteed Service (GS) tasks, while tasks with no hard requirements are referred to as Best Effort (BE) tasks. For GS tasks, we propose scheduling algorithms that provide deadline or computational power guarantees, or offer fair degradation in the QoS such tasks receive in case of congestion. Regarding BE tasks our objective is to allocate resources in a fair way, where fairness is interpreted in the max-min fair share sense. Though, we mainly address scheduling problems on computation resources, we also look at the joint scheduling of communication and computation resources and propose routing and scheduling algorithms aiming at co-allocating both resource type so as to satisfy their respective QoS requirements.