The development of radiation resistant materials for various nuclear applications and their performance under harsh environments has been central to many research efforts over the past decades. There still exist, however, large gaps in the understanding of fundamental modes of material degradation under extremes such as ion irradiation. We have shown that neutron total scattering measurements with pair distribution function (PDF) analysis can be utilized to uniquely characterize the structural properties of swift heavy ion irradiated materials, including complex (e.g., A2B2O7 pyrochlore) and simple oxides (e.g., AO2). Irradiation experiments were performed at the UNILAC accelerator of the GSI Helmholtz Center with heavy ions of specific energy of 8.6 MeV/u. Such projectiles produce the sufficiently large irradiated sample mass (~100 mg) needed for analysis at the Nanoscale Ordered Materials Diffractometer (NOMAD) beamline at the Spallation Neutron Source (Oak Ridge National Laboratory). Neutron probes enable detailed analysis of both cation and anion defect behavior, and short-range order, which is particularly important for investigating radiation effects with no long-range coherency. Recent results demonstrate that structural changes induced under irradiation are more complex than previously thought with distinct processes occurring over different length scales and a high degree of local atomic order. For example, disordered (crystalline) and amorphous pyrochlore oxides are composed of very similar atomic-scale building blocks despite the very different long-range structure, and ion beam-induced tetragonal zirconia is only a configurational averaged ensample of an orthorhombic nanodomains. These examples highlight the importance of short- and medium-range analysis for a comprehensive description of radiation effects in materials.