The rising demand for radiation detection materials in many applications has led to extensive research on scintillators1-3. The ability of a scintillator to absorb high-energy (kiloelectronvolt-scale) X-ray photons and convert the absorbed energy into low-energy visible photons is critical for applications in radiation exposure monitoring, security inspection, X-ray astronomy and medical radiography4,5. However, conventional scintillators are generally synthesized by crystallization at a high temperature and their radioluminescence is difficult to tune across the visible spectrum. Here we describe experimental investigations of a series of all-inorganic perovskite nanocrystals comprising caesium and lead atoms and their response to X-ray irradiation. These nanocrystal scintillators exhibit strong X-ray absorption and intense radioluminescence at visible wavelengths. Unlike bulk inorganic scintillators, these perovskite nanomaterials are solution-processable at a relatively low temperature and can generate X-ray-induced emissions that are easily tunable across the visible spectrum by tailoring the anionic component of colloidal precursors during their synthesis. These features allow the fabrication of flexible and highly sensitive X-ray detectors with a detection limit of 13 nanograys per second, which is about 400 times lower than typical medical imaging doses. We show that these colour-tunable perovskite nanocrystal scintillators can provide a convenient visualization tool for X-ray radiography, as the associated image can be directly recorded by standard digital cameras. We also demonstrate their direct integration with commercial flat-panel imagers and their utility in examining electronic circuit boards under low-dose X-ray illumination.