Metal halide perovskite single crystals hold promise for photovoltaics with high efficiency and stability due to their superior optoelectronic properties and weak bulk ion migration. The past several years have witnessed rapid development of single-crystal perovskite solar cells (PSCs) with efficiency rocketed from 6.5% to 24.3%, however, which still lags behind their polycrystalline counterparts. Moreover, the poor device stability under light illumination is contrary to the high ion migration barrier of perovskite single crystals. The key limiting factors should be the low crystalline quality and high surface defect density of solution-grown thin single crystals. Under this circumstance, a review paper summarizing the recent progress and challenges will be instructive for future development of this emerging field. In this manuscript, the crystal engineering used to enhance carrier transport and suppress carrier recombination in vertical single-crystal PSCs will be summarized initially, including crystal growth, component control, surface and interface modification. Subsequently, the application of perovskite single crystals in lateral single-crystal PSCs will be discussed and compared with the conventionally vertical structure. Finally, the challenges and proposed strategies for the development of single-crystal PSCs are provided.