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 layer-by-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 fields of 7 MV/cm in hexagonal quantum dots is evidenced by observations of various physical effects related to the quantum confined Stark effect, 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.