Our recent studies on asymmetric propargylic substitution reactions by using transition metal catalysts and organocatalysts are reviewed from the viewpoint of organic synthesis. Ruthenium and copper complexes bearing optically active ligands work as effective catalysts toward propargylic alkylation, paropargylic amination, propargylic etherification, propargylation of aromatic compounds, and related reactions to give the corresponding propargylic substituted products with a high enantioselectivity. Cooperative reactions by using both transition metal catalysts and organocatalysts are also described.