Keeping future generations safe from today's nuclear waste relies on this waste being effectively isolated for all time. Clay rocks, or rocks with a high clay content, offer promising isolation properties over time periods that are as long as the age of their host geological formations. Constructing a repository in such material does not significantly change the clay's isolation properties, which is a great advantage. Isolation is a function of the interplay between the slow release of radionuclides from the waste, the diffusion-controlled radionuclide migration, the establishment of a reducing geochemical environment, and the weak solubility and strong retention of the most toxic radionuclides on clay minerals and on additional engineered barrier materials.