III-nitrides based light-emitting diodes and laser diodes (LDs) have shown great success as solid-state lighting sources, but the development of common c-plane (0001) polar GaN emitters is facing limitations due to quantum-confinement Stark effect, efficiency drop, low efficiency at green range, and peak wavelength blue-shift. Efficient semipolar or nonpolar GaN light emitting diodes and LDs have been successfully demonstrated by growing on semipolar or nonpolar free-standing GaN substrates. The small size and high cost of high crystal quality semipolar or nonpolar free-standing GaN substrates, which are sliced from hydride vapor phase epitaxy grown c-plane bulk GaN substrate, have severely limited their commercial development and application. Achieving scalable heteroepitaxial semipolar GaN materials with a very low density of basal-stacking faults (BSFs) on a foreign substrate remains very challenging. The recent breakthrough in the demonstration of continuous-wave (CW) semipolar (202¯1) LDs at room-temperature on semipolar GaN/sapphire template marks a milestone in exploring high crystal quality heteroepitaxial semipolar GaN materials and low-cost semipolar emitters. Here, we review the key progress through the past years about the development of heteroepitaxial semipolar GaN materials including epitaxial lateral overgrowth, orientation controlling epitaxy, BSFs burying by neighboring Ga-polar (0001) GaN with air voids, facet-engineering orientation control epitaxy, resulting in a low density or free of basal stacking faults. Furthermore, we discuss the heteroepitaxially grown pulsed semipolar (112¯2) blue LDs and CW semipolar (202¯1) LDs.