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With the joint effort of the research community and industry companies, Grid computing has the potential to become a ubiquitous service that is accessible by everyone. Consequently, the policies to manage the allocation of limited computing resources to users become very important. End users will pay for the computation service they get, and choose from more than one grid service provider (GSP) based on their experiences with these GSPs; GSPs want to allocate the resources in a user-centric way to attract and retain users. During the resource allocation procedure, there are three most basic questions: "Where should one find the proper resources for users' jobs?", "When multiple jobs are waiting, which one should be scheduled first?", and "Given the hardware characteristics, how should jobs be further scheduled to maximize the utilization of hardware?" These questions lead to a natural hierarchical resource allocation scheme, which involves three levels: (1) Find the proper resources for the proper jobs, (2) prioritize and schedule jobs to execute in a reasonable order, and (3) coordinate jobs to execute on the hardware efficiently. This paper reviews and classifies related work, and suggests future research directions.