Scintillators are materials that convert ionizing radiation in the form of particles or photons into low-energy photons in the ultraviolet to near-infrared spectral range. This work reviews efforts to use colloidal nanocrystals as scintillator materials. To date, research on colloidal nanocrystals as scintillators has focused on doped phosphor systems, quantum dots and related structures, and perovskite-based nanocrystals. Among various material classes and forms, colloidal semiconductor nanocrystals stand out thanks to their appealing fluorescence properties, yet understanding of their radioluminescence and cathodoluminescence is incomplete. This review discusses fundamental limits and material design challenges toward achieving high brightness, fast speed, and durable scintillator performance with nanocrystal scintillators. First, this review describes the basic principles and efficiency limitations of scintillation, particularly the large influence of multiple exciton generation in many nanocrystal species, as well as performance metrics. Second, methods for measurement are described. Third, we review the results of the main classes of nanocrystal scintillators, including quantum dots and related particles, perovskites, and doped-phosphor particles. Fourth, scintillation imaging is discussed in terms of the relevant performance metrics and results obtained using nanocrystal materials. Finally, we note the strengths and weaknesses of nanocrystal scintillators and discuss potential areas of further development.