In this account, we describe series of our research on a Lewis acid-catalyzed insertion reaction of α-diazo esters into a carbon–carbon bond or a carbon–halogen bond. Indium catalysts mediated not only the insertion of α-diazo esters into a carbon–carbon bond of alkyl acetates, alkyl ethers, acetals, and alkyl halides, but also a carbon–halogen bond of alkyl chlorides, bromides, and iodides. BF3 specifically accelerated the insertion of α-diazo esters into a carbon–fluorine bond. The key of this catalysis is acetate, alkoxide, and halide shuttle systems mediated by a Lewis acid, in which a Lewis acid abstracts a leaving group from a starting substrate and releases the leaving group to the appropriate carbocation intermediate in the catalytic cycle.