Ultraviolet photodetectors have applications in fields such as medicine, communications and defence(1), and are typically made from single-crystalline silicon, silicon carbide or gallium nitride p-n junction photodiodes. However, such inorganic photodetectors are unsuitable for certain applications because of their high cost and low responsivity (<0.2 AW(-1))(2). Solution-processed photodetectors based on organic materials and/or nanomaterials could be significantly cheaper to manufacture, but their performance so far has been limited(2-7). Here, we show that a solution-processed ultraviolet photodetector with a nanocomposite active layer composed of ZnO nanoparticles blended with semiconducting polymers can significantly outperform inorganic photodetectors. As a result of interfacial trap-controlled charge injection, the photodetector transitions from a photodiode with a rectifying Schottky contact in the dark, to a photoconductor with an ohmic contact under illumination, and therefore combines the low dark current of a photodiode and the high responsivity of a photoconductor (similar to 721-1,001 AW(-1)). Under a bias of <10 V, our device provides a detectivity of 3.4x10(15) Jones at 360 nm at room temperature, which is two to three orders of magnitude higher than that of existing inorganic semiconductor ultraviolet photodetectors.