Most work on this subject is based on the use of alcohols as reagents in the presence of enantiomerically pure nucleophilic catalysts [1,2]. This section is subdivided into four parts on the basis of classes of anhydride substrate and types of reaction performed (Scheme 13.1) -desymmetrization of prochiral cyclic anhydrides (Section 13.1.1); kinetic resolution of chiral, racemic anhydrides (Section 13.1.2); parallel kinetic resolution of chiral, racemic anhydrides (Section 13.1.3); and dynamic kinetic resolution of racemic anhydrides (Section 13.1.4).Desymmetrization of prochiral cyclic anhydrides: In the presence of the chiral nucleophilic catalyst (e.g. A, Scheme 13.1, top) one of the enantiotopic carbonyl groups of the prochiral (usually meso) cyclic anhydride substrate is selectively converted into an ester. Application of catalyst B (usually the enantiomer or a pseudoenantiomer of A) results in generation of the enantiomeric product ester. Ideally, 100% of one enantiomerically pure product can be generated from the starting anhydride. No reports of desymmetrizing alcoholyses of acyclic meso anhydrides appear to exist in the literature.Kinetic resolution of chiral, racemic anhydrides: In this process the racemic mixture of a chiral anhydride is exposed to the alcohol nucleophile in the presence of a chiral catalyst such as A (Scheme 13.2, middle). Under these conditions, one substrate enantiomer is converted to a mono-ester whereas the other remains unchanged. Application of catalyst B (usually the enantiomer or a pseudo-enantiomer of A) results in transformation/non-transformation of the enantiomeric starting anhydride(s). As usual for kinetic resolution, substrate conversion/product yield(s) are intrinsically limited to a maximum of 50%. For ''normal'' anhydrides (X ¼ CR 2 ), both carbonyl groups can engage in ester formation, and the product formulas in Scheme 13.1 are drawn arbitrarily. This section also covers the catalytic asymmetric alcoholysis of a-hydroxy acid O-carboxy anhydrides (X ¼ O) and of a-amino acid Ncarboxy anhydrides (X ¼ NR). In these reactions the electrophilicity of the carbonyl groups flanking ''X'' is reduced and regioselective attack of the alcohol nucleophile on the other carbonyl function results.Parallel kinetic resolution of chiral, racemic anhydrides: The term parallel kinetic resolution (PKR) implies that the two substrate enantiomers (Scheme 13.1, bottom 50 mol-% catalyst 2 CH 3 OH, toluene, r.t., 2h 7; 57 %, 76 % ee 6 Aitken et al. (refs. 7,8) Scheme 13.2 13.1 Desymmetrization and Kinetic Resolution of Cyclic Anhydrides 349 93 98 97 91 84 94 91 50 71 72 Ph Scheme 13.36 13.4 Desymmetrization of meso-Epoxides 381