There have been significant recent developments in the growth of single-crystal gallium nitride (GaN) on unconventional templates for large-area blue or green light-emitting diodes (LEDs) which, together with layer transfer onto foreign substrates, can enable flexible and stretchable lighting applications. Here, the heteroepitaxial growth of GaN on amorphous and single-crystal substrates employing various interlayers and nucleation layers is reviewed, as well as the use of weak interfaces for layer-transfer onto foreign substrates. Recent progress in low-temperature GaN-based red-green-blue (RGB) LEDs on glass substrates, which has exhibited a calculated efficiency of 11% compared with that from commertial LEDs, is discussed. Layer-transfer techniques with various interlayers are also discussed. These heteroepitaxial GaN growth and layer-transfer technologies are expected to lead to new lighting and display devices with high efficiency and full-color tunability, which are suitable for large-area, stretchable display and lighting applications.