Nanowires are rod or whisker-like structures with length on the order of microns and diameter from tens to hundreds of nanometers.  They represent a new class of three-dimensional materials, and the next step in the evolution of conventional two-dimensional thin films, quantum wells, or heterostructures. Nanowires are typically fabricated by the assistance of foreign metal catalysts, such as Au, that collect deposited material, resulting in localized growth of nanowires. However, the use of foreign metal particles can result in contamination of the nanowires and reduction in the carrier lifetime, which degrades device performance. In the present work, we present the self-assisted growth of GaP nanowires by molecular beam epitaxy, using Ga droplets as a seed particle without the use of any foreign metal catalysts.  Growth of the nanowire occurs by selective-area epitaxy using a patterned array of holes in an SiO_x mask. The holes collect Ga adatoms forming a Ga droplet that seeds the nanowire growth. The size of the Ga droplet can be controlled by a novel evaporation process, resulting in ultra-thin nanowire structures.  GaAs heterostructures were introduced into the GaP nanowires during growth resulting in quantum dots.  The quantum dots are encapsulated in GaP, resulting in passivation of the QD surfaces.  Photoluminescence emission was observed from the QDs in the visible range.  The emission wavelength is tunable by the size or composition of the QDs.  This process results in controlled luminescence emission with application in single photon sources, light emitting diodes, or laser diodes.