Performance assessment of nuclear waste disposal options requires implementation of effective buffer materials. Buffer materials must meet longevity requirements and scavenge challenging radioisotopes, e.g., iodine-129 (I-129) and technetium-99 (Tc-99), both long-lived, highly mobile, anionic species in oxic environments. In many proposed nuclear waste repositories, heat generating radioactive waste will be surrounded by clay buffer material, which swells to fill the gap between the waste package and the host geology, restricting radionuclide transport to diffusive processes for several hundred years. The clay can be functionalized to further the limit release of Tc-99, as pertechnetate (TcO4–), and I-129, as iodate (IO3–) and iodide (I–). Here, we review clay buffer functionalization and the potential to enhance sequestration of anionic radionuclides that have an increased risk of leaching out of a disposal facility. Functionalization with quaternary amines, nanosilver, bismuth-based materials, silane, and aluminum pillars have been demonstrated to improve the removal of targeted contaminants from solution. This review defines key research questions that remain: (i) can functionalized clay immobilize TcO4–, IO3–, and I– to the same extent as the reactive components themselves? (ii) Does functionalization affect the ability of the clay barrier to perform its safety functions of protecting the waste canister and limiting radionuclide transport? In addition to radionuclide retention, a multimodal analytical approach is required to assess functionalized clay performance, and recommended techniques are reviewed here. The key parameters that can influence radionuclide sequestration by functionalized clay are also evaluated. Theoretical approaches, including both density functional theory calculations and molecular dynamics simulations, can inform the energetics and kinetics of radionuclide interactions with functionalized clays. This combined experimental and theoretical approach can link atomistic and microscopic processes to predict the macroscopic physical properties of the functionalized clays.