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This paper explores asynchrony in the context of high performance computing. We explore where asynchrony comes from, why it matters, and how exascale computing impacts our consideration of asynchrony. We present a list of key concepts that are expected to permit practical exascale computing in the presence of asynchrony. We then introduce the ParalleX execution model along with its open source runtime system implementation, High Performance ParalleX (HPX). Performance examples of HPX using open source benchmarks are then presented.