Several unsolved challenges in radio-frequency heating and current drive are highlighted. These include current drive in magnetic geometries in which the toroidal magnetic field cannot be assumed to be dominant, current start-up with hyperresistivity, current drive with oscillating parameters, and synergistic effects between current drive and alpha channeling. These challenges are not necessarily straightforward to address, and it is possible that the challenges cannot even be met, but were they met, at least in some cases, there is the potential of significant consequence.