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This paper reviews both experimental and theoretical work on nanostructures showing high quantum yields due to the phenomenon of multiple exciton generation. It outlines the aims and barriers to progress in identifying further such nanostructures and also includes important developments concerning solar devices where nanostructures act as the light-absorbing component. It reports on both semiconductor and carbon structures, both monocomposite (of various dimensionalities) and heterogeneous. Finally, it looks at future directions that can be taken to push solar cell efficiency above the classic limit set by Shockley and Queisser in 1961.