Recent works by our group on hexagonal and cubic GaN/AlN quantum dots grown by molecular beam epitaxy are reviewed. It is shown that the growth of GaN on AlN can occur either in a layerby- layer mode to form quantum wells or in the Stranski-Krastanow mode to form self-assembled quantum dots. High resolution transmission electron microscopy reveals that quantum dots are truncated pyramids (typically 3 nm high and 15 nm wide), nucleating on top of a wetting layer. The existence of internal electric elds of 7 MV/cm in hexagonal quantum dots is evidenced by observations of various physical e ects related to the quantum con ned Stark e ect, e.g. energy redshift of the interband transition, decrease of its oscillator strength, or enhancement of the exciton interaction with LO phonons. Prospects for UV and near-IR applications, using interband and intersubband transitions of GaN/AlN quantum dots, respectively, will be discussed also in this presentation.