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This paper discusses the material to be presented by H. J. Siegel in his keynote talk. Distributed high-performance heterogeneous computing (HC) environments are composed of machines with varied computational capabilities interconnected by high-speed links. These environments are well suited to meet the computational demands of large, diverse groups of applications. One key factor in achieving the best performance possible from HC environments is the ability to assign effectively the applications to machines and schedule their execution. Several factors must be considered during this assignment. A conceptual model for the automatic decomposition of an application into tasks and assignment of tasks to machines is presented. An example of a static matching and scheduling approach for an HC environment is summarized. Some examples of current HC technology and open research problems are discussed.