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This paper discusses new research directions leading to novel software technologies for the development and runtime support of complex applications executing on dynamic and adaptive computing platforms. The two key technology areas discussed here are new compiling technology and new application composition technology, which will enable applications to effectively exploit such platforms. In the new compiling system advocated here, a tight interaction loop is enabled between the compiler and the underlying system resource managers, as well as performance descriptors of the applications and the underlying hardware and software systems. This kind of new compiling system will have the ability to adaptively optimize the mapping of applications on the underlying dynamic platform assembly. In addition, the paper discusses the need for new technology for knowledge-based, compiler-invoked application components' dynamic assembly. Together with such advances, new programming models that can aid the new compiling system in the tasks above are also necessary. The paper also addresses the need for integration of these technologies into application support environments and demonstration of the technologies on important production-class applications.