Beyond the unprecedented success achieved in photovoltaics (PVs), lead halide perovskites (LHPs) have shown great potential in other optoelectronic devices. Among them, nanometer-scale perovskite quantum dots (PQDs) with fascinating optical properties including high brightness, tunable emission wavelength, high color purity, and high defect tolerance have been regarded as promising alternative down-conversion materials in phosphor-converted light-emitting diodes (pc-LEDs) for lighting and next-generation of display technology. Despite the promising applications of perovskite materials in various fields, they have received strong criticism for the lack of stability. The poor stability has also attracted much attention. Within a few years, numerous strategies towards enhancing the stability have been developed. This review summarizes the mechanisms of intrinsic- and extrinsic-environment-induced decomposition of PQDs. Simultaneously, the strategies for improving the stability of PQDs are reviewed in detail, which can be classified into four types: (1) compositional engineering; (2) surface engineering; (3) matrix encapsulation; (4) device encapsulation. Finally, the challenges for applying PQDs in pc-LEDs are highlighted, and some possible solutions to improve the stability of PQDs together with suggestions for further improving the performance of pc-LEDs as well as the device lifetime are provided.