The optically active 3-oxobutylideneaminato transition-metal complexes have been developed as efficient catalysts for a variety of enantioselective reactions; e.g. the corresponding manganese(III) complexes catalyzed the enantioselective aerobic epoxidation of unfunctionalized olefins, and the corresponding cobalt complexes have been developed for the enantioselective borohydride reduction of various carbonyl compounds. The cobalt complexes could also be employed for the catalytic enantioselective cyclopropanation with diazoacetates and the Lewis acid catalyses such as the hetero Diels-Alder reaction, carbonyl-ene reaction, and 1,3-dipolar cycloaddition of nitrones. In the presence of the cobalt complex, the Henry reaction proceeded with a high enantioselectivity, and the enantioselective chemical fixation of carbon dioxide to obtain the optically active cyclic carbonate. In these Lewis acid catalyses, the valence of cobalt and the counter anion have significant effects on the reaction rate and stereoselectivity. q