Hydrogen-bridged radical cations (HBRCs) are an intriguing subclass of ion–molecule complexes. They may act as key intermediates of remarkable stability in both association and dissociation reactions of heteroatom-containing molecular ions. The H-bridge of such an HBRC can promote isomerization of its ionic component by H-transfer. Proton-transport catalysis (PTC) is a prime example. Here, a neutral molecule promotes the smooth transformation of an ion into its H-shift isomer by consecutive proton-transfer reactions. A celebrated case is the water-catalyzed isomerization of CH3OH•+ into its more stable distonic isomer •CH2OH2+. Other early studies of PTC also deal with catalyzing 1,2-H shifts in association reactions. This short review focuses on more recent combined experimental and computational studies of catalysis in HBRCs. Mechanisms involving both proton and H atom transfers have been proposed for a variety of systems of H-shift isomers. It has also become clear that PTC is not confined to bimolecular reactions. It also features in the unimolecular chemistry of heteroatom-containing ions, which have a tendency to isomerize to HBRCs en route to their dissociation.