GaInN/GaN heterostructures have been grown by molecular beam epitaxy (MBE) on c-plane sapphire substrates. The growth of Ga1-xInxN (x > 12%) alloy has been extensively studied. At low V/III ratio, the growth undergoes a Stranski-Krastanov transition giving rise to the formation of three-dimensional (3D) islands. On the other hand, a high V/III ratio promotes the two-dimensional (2D) layer-by-layer growth regime. The optical properties of Ga1-xInxN (x > 12%)/GaN heterostructures made from either a 3D GaInN layer or a 2D GaInN layer are similar. This indicates that the mechanism responsible for the peculiar optical properties of Ga1-xInxN (x > 12%)/GaN heterostructures is intrinsically due to sell-formed quantum dots (QDs) that may arise from In clustering in the GaInN alloy. Actually, the properties of the GaInN/GaN QDs grown by MBE are very close to those grown by metal-organic chemical vapor deposition (MOCVD). As for MOCVD material, a high radiative efficiency is obtained correlatively with a giant Stokes shift and a very large carrier lifetime. The high efficiency of GaInN/GaN QDs is confirmed by gain measurements performed at room temperature. Finally, light-emitting diodes (LEDs) based on GaInN QDs have been fabricated. They demonstrate improved performances compared to LED based on homogeneous GaInN alloys.