Abstract Salt-fingering is a potentially important mechanism for mixing different water-masses in those parts of the ocean where warm salty waters overlie cooler fresher. This review surveys advances in salt-fingering theory as they pertain to ocean mixing. Basic equations are presented along with steady, maximum buoyancy-flux and fastest-growing finger solutions. Attempts to quantify theoretically finger-induced fluxes of heat, salt and buoyancy, and to understand staircase formation and maintenance, are described. Also considered are the confounding influences of internal wave shear and strain, and intermittent internal-wave shear-driven turbulence, which are present in the ocean but in few theories. Finally, outstanding theoretical questions about the role of salt fingers in the ocean are raised.