Here we provide a comprehensive review of a newly developed lighting technology based on metal halide perovskites (i.e. perovskite light-emitting diodes) encompassing the research endeavours into materials, photophysics and device engineering. At the outset we survey the basic perovskite structures and their various dimensions (namely three-, two- and zero-dimensional perovskites), and demonstrate how the compositional engineering of these structures affects the perovskite light-emitting properties. Next, we turn to the physics underpinning photo- and electroluminescence in these materials through their connection to the fundamental excited states, energy/charge transport processes and radiative and non-radiative decay mechanisms. In the remainder of the review, we focus on the engineering of perovskite light-emitting diodes, including the history of their development as well as an extensive analysis of contemporary strategies for boosting device performance. Key concepts include balancing the electron/hole injection, suppression of parasitic carrier losses, improvement of the photoluminescence quantum yield and enhancement of the light extraction. Overall, this review reflects the current paradigm for perovskite lighting, and is intended to serve as a foundation to materials and device scientists newly working in this field.