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This chapter summarizes a variety of the important advances using chiral phosphoric acids as catalysts for enantioselectively controlled reactions (asymmetric catalysis). It will be evident that the variety of substrates and nucleophiles is quite large, so only a selected summary is shown. Exhaustive reviews have been addressed previously. The reactions have been described by nucleophile types (carbon, oxygen, sulfur, and nitrogen), and also by types of electrophiles (imines, oxonium ions etc.) or by specific reaction types (pericyclic and phase-transfer reaction types, and atroposelective processes). In addition, the various types of addition modes are addressed and commented on through the chapter. We hope that the reader can gain a good grasp of how phosphorous is one of the most important elements for organocatalysis; its impact is only now starting to be fully exploited on the forefront of asymmetric catalysis.

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