Emission mechanisms of a device-quality quantum well (QW) structure and bulk three dimensional (3D) InGaN materials grown on sapphire substrates without any epitaxial lateral overgrown GaN base layers were investigated. The InxGa1-xN layers showed various degrees of in-plane spatial potential (band gap) inhomogeneity, which is due to a compositional fluctuation or a few monolayers thickness fluctuation. The degree of fluctuation changed remarkably around a nominal InN molar fraction x=0.2, which changes to nearly 0.08-0.1 for the strained InxGa1-xN. This potential fluctuation induces localized energy states both in the QW and 3D InGaN, showing a large Stokes-like shift. The spontaneous emission from undoped InGaN single QW light-emitting diodes (LEDs), undoped 3D LEDs, and multiple QW (MQW) laser diode (LD) wafers was assigned as being due to the recombination of excitons localized at the potential minima, whose lateral size was determined by cathodoluminescence mapping to vary from less than 60 to 300 nm in QWs. Those structures are referred to as quantum disks (Q disks) or segmented QWs depending on the lateral size. Blueshift of the emission peak by an increase of the driving current was explained to be combined effects of band filling of the localized states by excitons and Coulomb screening of the quantum confined Stark effect induced by the piezoelectric field. The lasing mechanisms of the continuous wave In0.15Ga0.85N MQW LDs having small potential fluctuations can be described by the well-known electron-hole-plasma (EHP) picture. However, the inhomogeneous MQW LDs are considered to lase by EHP in segmented QWs or Q disks. It is desirable to use entire QW planes with small potential inhomogeneity as gain media for higher performance LD operation.