An emerging trend in computing is to use distributed heterogeneous computing (HC) systems to execute a set of tasks. Cluster computer systems, grids, and Desktop Grids are three popular kinds of HC systems. An important component of an HC system is its resource management system (RMS). The main responsibility of an RMS is assigning resources to tasks in order to satisfy certain performance requirements. For cluster computer systems, we propose a new mapping heuristic which requires less state information than current heuristics. For Desktop Grids, we propose a new scheduling policy that exploits knowledge of the effective computing power delivered by the machines and the distribution of their fault times in order to improve performance. Finally, for grids, we propose a new decentralized load balancing policy which dramatically cuts down the communication overhead incurred in state information update. The proposed resource management policies utilize the solution to a linear programming problem (LP) which maximizes the system capacity. Our simulation experiments show that these policies perform very competitively, especially in highly heterogeneous systems. / Thesis / Doctor of Philosophy (PhD)