Halide perovskite is one of the most promising semiconducting materials in a variety of fields such as solar cells, photodetectors, and light-emitting diodes. Lead halide perovskite single crystals featuring long diffusion length, high carrier mobility, large light absorption coefficient and low defect density, have been attracting increasing attention. Fundamental study of the intrinsic nature keeps revealing the superior optoelectrical properties of perovskite single crystals over their polycrystalline thin film counterparts, but to date, the device performance lags behind. The best power conversion efficiency (PCE) of single crystal-based solar cells is 21.9%, falling behind that of polycrystalline thin film solar cells (25.2%). The oversized thickness, defective surfaces, and difficulties in depositing functional layers, hinder the application of halide perovskite single crystals in optoelectronic devices. Efforts have been made to synthesize large-area single crystalline thin films directly on conductive substrates and apply defect engineering approaches to improve the surface properties. This review starts from a comprehensive introduction of the optoelectrical properties of perovskite single crystals. Then, the synthesis methods for high-quality bulk crystals and single-crystalline thin films are introduced and compared, followed by a systematic review of their optoelectronic applications including solar cells, photodetectors, and X-ray detectors. The challenges and strategical approaches for high-performance applications are summarized at the end with a brief outlook on future work.