Different from the case of GaN or AlGaN alloys, the near-band-edge (NBE) emission of quantum wells (QWs) and even epilayers of InxGa1- xN alloys of low InN mole fractions (x) exhibits high quantum-efficiency (QE) against the presence of threading dislocations (TDs) as high as 109 cm-2. Accordingly InxGa1- xN alloys are exclusively used as an active region of green to ultraviolet light-emitting diodes (LEDs) and laser diodes, as well as the heart of white LEDs. Here, current understandings on the emission mechanisms of InxGa1- xN QWs, especially the defect-tolerant emission probability of localized excitons, are reviewed. There exist three disadvantages in obtaining high QE, namely a high density of TDs that cause the nonradiative recombination, kinetic immiscibility of In-containing alloys that introduces high-concentration Shockley-Read-Hall nonradiative recombination centers (NRCs) consisting of vacancy complexes, and high internal electric-fields across the QWs induced by the polarization discontinuities at heterointerfaces along the c-axis, which decrease the radiative recombination rate. The use of InxGa1- xN alloys of low x overcomes such disadvantages with the aid of In-originated localization effects that prevent excitons from trapping by TDs or NRCs. Simultaneous observation of short diffusion length and sufficiently long nonradiative recombination lifetime at room temperature indicates strong localization of holes or excitons.