Energy-dispersive X-ray diffraction (EDXRD) is extremely insensitive to sample morphology when implemented in a back-reflection geometry. The capabilities of this non-invasive technique for cultural heritage applications have been explored at high resolution at the Diamond Light Source synchrotron. The results of the XRD analysis of the pigments in 40 paints, commonly used by 20th century artists, are reported here. It was found that synthetic organic pigments yielded weak diffraction patterns at best, and it was not possible to unambiguously identify any of these pigments. In contrast, the majority of the paints containing inorganic pigments yielded good diffraction patterns amenable to crystallographic analysis. The high resolution of the technique enables the extraction of a range of detailed information: phase identification (including solid solutions), highly accurate unit cell parameters, phase quantification, crystallite size and strain parameters and preferred orientation parameters. The implications of these results for application to real paintings are discussed, along with the possibility to transfer the technique away from the synchrotron and into the laboratory and museum through the use of state-of-the-art microcalorimeter detectors. The results presented demonstrate the exciting potential of the technique for art history and authentication studies, based on the non-invasive acquisition of very high quality crystallographic data.