p-Type doping represents a key step towards III-nitride (InN, GaN, AlN) optoelectronic devices. In the past, tremendous efforts have been devoted to obtaining high quality p-type III-nitrides, and extraordinary progress has been made in both materials and device aspects. In this article, we intend to discuss a small portion of these processes, focusing on the molecular beam epitaxy (MBE)-grown p-type InN and AlN-two bottleneck material systems that limit the development of III-nitride near-infrared and deep ultraviolet (UV) optoelectronic devices. We will show that by using MBE-grown nanowire structures, the long-lasting p-type doping challenges of InN and AlN can be largely addressed. New aspects of MBE growth of III-nitride nanostructures are also discussed.