Cerium dioxide (CeO2) exhibits complex behavior when irradiated with swift heavy ions. Modifications to this material originate from the production of atomic-scale defects, which accumulate and induce changes to the microstructure, chemistry, and material properties. As such, characterizing its radiation response requires a wide range of complementary characterization techniques to elucidate the defect formation and stability over multiple length scales, such as X-ray and neutron scattering, optical spectroscopy, and electron microscopy. In this article, recent experimental efforts are reviewed in order to holistically assess the current understanding and knowledge gaps regarding the underlying physical mechanisms that dictate the response of CeO2 and related materials to irradiation with swift heavy ions. The recent application of novel experimental techniques has provided additional insight into the structural and chemical behavior of irradiation-induced defects, from the local, atomic-scale arrangement to the long-range structure. However, future work must carefully account for the influence of experimental conditions, with respect to both sample properties (e.g., grain size and impurity content) and ion-beam parameters (e.g., ion mass and energy), to facilitate a more direct comparison of experimental results.