The combination of transition-metal complexes and Lewis acids has been recently applied to several catalytic reactions, in which the Lewis acid plays a crucial role as a non-innocent additive to accelerate the reaction. In this review article, the reasons for the acceleration by the Lewis acid are discussed based on our recent theoretical studies. In the H-H σ-bond activation of a dihydrogen molecule by a nickel(0)-borane complex, the empty p orbital of the borane moiety interacts with the H-H σ bonding MO to form charge transfer (CT) from the dihydrogen molecule to the borane moiety to accelerate the reaction. In the B-F σ-bond activation of BF by a platinum(0)-bisphosphine complex, the second BF molecule interacts with the F atom that is dissociating from the B atom to stabilize the transition state and product by the CT from the F atom to the second BF . In this reaction, the substrate BF plays a crucial role as the Lewis acid to accelerate the activation of the B-F σ bond. In the nickel-catalyzed decyanative coupling of arylcarboxybenzonitriles with acetylenes, two molecules of the aluminum Lewis acid interact with the cyano N atom and the carbonyl O atom of the substrate to stabilize the transition state and intermediate. In the nickel-catalyzed alkylation of aromatic amides with alkenes, the Lewis acid enhances the para regioselectivity of alkylation by interacting with the carbonyl O atom. In the nickel-catalyzed carboxylation of sp carbon and sp carbon atoms with carbon dioxide, not the σ-bond activation but the insertion reaction of carbon dioxide into the metal-carbon bond is accelerated by the Lewis acid by interacting with the O atom of carbon dioxide, because the CT from the metal-carbon bond to carbon dioxide is enhanced by the interaction. This theoretical knowledge suggests that the combination of transition-metal complex and Lewis acid can broaden the application range of transition-metal complex as catalyst.