Metal halide perovskites have shown excellent optoelectronic properties, including high photoluminescence quantum yield, tunable emission wavelengths, narrow full-width at half-maximums and a low-cost, solution-processed fabrication, which make it exhibit great potential as emission-layer materials of light-emitting diodes. With the joint efforts of researchers from different disciplines, there has been a significant progress in the improvement in the external quantum efficiency (EQE) and stability of perovskite light-emitting diodes (PeLEDs) in recent years, especially in green PeLEDs with EQEs over 30%. However, their operational stability lags behind other commercial organic and chalcogenide quantum dot emitters, limiting their practical application. In this review, we first introduce the basic device structure of PeLEDs, as well as the factors influencing the EQE and stability of PeLEDs. Secondly, the development of lead-based and lead-free PeLEDs are summarized systematically. Thirdly, challenges of PeLEDs are discussed in detail, including low the EQE of blue PeLEDs, poor device stability and EQE roll-off. Finally, some suggestions and perspectives for future research directions for PeLEDs are proposed.