AbstractUltralow trap densities, exceptional optical and electronic properties have been reported for lead halide perovskites single crystals; however, ambiguities in basic properties, such as the band gap, and the electronic defect densities in the bulk and at the surface prevail. Here, we synthesize single crystals of methylammonium lead bromide (CH₃NH₃PbBr₃), characterise the optical absorption and photoluminescence and show that the optical properties of single crystals are almost identical to those of polycrystalline thin films. We observe significantly longer lifetimes and show that carrier diffusion plays a substantial role in the photoluminescence decay. Contrary to many reports, we determine that the trap density in CH₃NH₃PbBr₃ perovskite single crystals is 10¹⁵ cm⁻³_, only one order of magnitude lower than in the thin films. Our enhanced understanding of optical properties and recombination processes elucidates ambiguities in earlier reports, and highlights the discrepancies in the estimation of trap densities from electronic and optical methods.