New photovoltaic materials have been searched for in the past decades for clean and renewable solar energy conversion with an objective of reducing the levelized cost of electricity (that is, the unit price of electricity over the course of the device lifetime). An emerging family of semiconductor materials — organic–inorganic halide perovskites (OIHPs) — are the focus of the photovoltaic research community owing to their use of low cost, nature-abundant raw materials, low-temperature and scalable solution fabrication processes, and, in particular, the very high power conversion efficiencies that have been achieved within the short time of their development. In this Review, we summarize and critically assess the most recent advances in understanding the physical properties of both 3D and low-dimensional OIHPs that favour a small open-circuit voltage deficit and high power conversion efficiency. Several prominent topics in this field on the unique properties of OIHPs are surveyed, including defect physics, ferroelectricity, exciton dissociation processes, carrier recombination lifetime and photon recycling. The impact of ion migration on solar cell efficiency and stability are also critically analysed. Finally, we discuss the remaining challenges in the commercialization of OIHP photovoltaics. This Review summarizes advances in understanding the unique physical properties of hybrid perovskites that enable the fabrication of high-efficiency solar cells with high open-circuit voltages, which is crucial for their further development towards commercialization.