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All modern computers are designed using the 'von Neumann' architecture and built using silicon transistor technology. Both architecture and technology have been remarkably successful. Yet there are a range of problems for which this conventional architecture is not particularly well adapted, and new architectures are being proposed to solve these problems, in particular based on insight from nature. Transistor technology has enjoyed 50 years of continuing progress. However, the laws of physics dictate that within a relatively short time period this progress will come to an end. New technologies, based on molecular and biological sciences as well as quantum physics, are vying to replace silicon, or at least coexist with it and extend its capability. The paper describes these novel architectures and technologies, places them in the context of the kinds of problems they might help to solve, and predicts their possible manner and time of adoption. Finally it describes some key questions and research problems associated with their use.