We studied palladium- or iridium-catalyzed allylation as an effective method for the asymmetric synthesis of alpha-amino acids, hydroxylamines, oximes, and amines. The stereochemistry of the palladium-catalyzed allylic alkylation of a prochiral diphenylimino glycinate was controlled by chiral PTC, and gave chiral amino acids. In contrast, iridium-catalyzed allylic substitution of diphenylimino glycinate proceeded with good enantio- and diastereo-selectivities with a new bidentate chiral ligand to give a novel method for preparing two branched diastereoisomers by simply switching the base. For the synthesis of alpha,alpha-disubstituted amino acids, the palladium-catalyzed tandem reaction of dehydroamino acids was developed based on radical chemistry. Next, the viability of oximes and hydroxylamines as oxygen atom nucleophiles in transition metal-catalyzed allylic substitutions was examined. Regio- and enantioselective allylic substitution of oximes and hydroxylamines was achieved by using the iridium complex of chiral pybox ligand. Sequential allylic amination gave a novel method for preparing azacycles. Finally, umpolung allylation with aldehyde or imine was studied by using palladium catalyst and indium iodide. The palladium-indium iodide-mediated reaction of chiral 2-vinylaziridines with aldehydride proceeded with excellent diastereoselectivity. The role of water in directing the diastereo- or regioselectivities was investigated in the allylation and propargylation of chiral oxime ether, The allylation of oxime ether with monosubstituted allylic reagents afforded either gamma-adduct or alpha-adduct depending on the reaction conditions.