III-nitride light-emitting devices have been subjects of intense research for the last several decades owing to the versatility of their applications for fundamental research, as well as their widespread commercial utilization. Nitride light-emitters in the form of light-emitting diodes (LEDs) and lasers have made remarkable progress in recent years, especially in the form of blue LEDs and lasers. However, to further extend the scope of these devices, both below and above the blue emission region of the electromagnetic spectrum, and also to expand their range of practical applications, a number of issues and challenges related to the growth of materials, device design, and fabrication need to be overcome. This review provides a detailed overview of nitride-based LEDs and lasers, starting from their early days of development to the present state-of-the-art light-emitting devices. Besides delineating the scientific and engineering milestones achieved in the path towards the development of the highly matured blue LEDs and lasers, this review provides a sketch of the prevailing challenges associated with the development of long-wavelength, as well as ultraviolet nitride LEDs and lasers. In addition to these, recent progress and future challenges related to the development of next-generation nitride emitters, which include exciton-polariton lasers, spin-LEDs and lasers, and nanostructured emitters based on nanowires and quantum dots, have also been elucidated in this review. The review concludes by touching on the more recent topic of hexagonal boron nitride-based light-emitting devices, which have already shown significant promise as deep ultraviolet and single-photon emitters.