Most efficient perovskite solar cells are based on polycrystalline thin films; however, substantial structural disorder and defective grain boundaries place a limit on their performance. Perovskite single crystals are free of grain boundaries, leading to significantly low defect densities, and thus hold promise for high-efficiency photovoltaics. However, the surfaces of perovskite single crystals present a major performance bottleneck because they possess a higher density of traps than the bulk. Hence, it is crucial to understand and control the surface trap population to fully exploit perovskite single crystals. This Perspective highlights the importance of surface-trap management in unleashing the potential of perovskite single-crystal photovoltaics and discusses strategies to take this technology beyond the proof-of-concept stage.