The group III-nitride (InN, GaN, and AlN) class of semiconductors has become one of two that are critical to a number of technologies in modern life—the other being silicon. Light-emitting diodes made from (In,Ga)N, for example, dominate recent innovations in general illumination and signaling. Even though the (In,Ga)N materials system is fairly well established and widely used in advanced devices, challenges continue to impede development of devices that include aluminum-containing nitride films such as (Al,Ga)N. The main difficulty is efficient doping of films with aluminum-rich compositions; the problem is particularly severe for p-type doping, which is essential for Ohmic contacts to bipolar device structures. This review briefly summarizes the fundamental issues related to p-type doping, and then discusses a number of approaches that are being pursued to resolve the doping problem or for circumventing the need for p-type doping. Finally, we discuss an approach to doping under liquid-metal-enabled growth by molecular beam epitaxy. Recent results from a number of groups appear to indicate that p-type doping of nitride films under liquid-metal-enabled growth conditions might offer a solution to the doping problem—at least for materials grown by molecular beam epitaxy.