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It has been several years since InGaN/GaN light-emitting diodes (LEDs) on nonpolar and semipolar orientations were first demonstrated. Prominent performance and inherent potential of these crystallographic orientations have been revealed as bulk-GaN substrates of arbitrary orientations became available for epitaxial device growth. At this point in time, we intend to survey the progress made to date and prospect the future requirements for further device improvements. The discussion begins with a historical background: how nonpolar/semipolar orientations were introduced to III-nitride LEDs and why they are beneficial. The discussion then provides information on elementary crystallography and piezoelectricity in addition to the electronic band structure of wurtzite crystals. Later in this paper, LED reports are collected to develop comprehensive knowledge of the past research efforts and trends. Nonpolar and semipolar orientations provide not only high LED performances, e.g., optical output power and wavelength ranges, but also unique functions, e.g., polarized light emission, which will explore new fields of applications.