At present two ideologies appear to govern the international selection of concepts for isolation of radionuclides escaped from High-Level Radioactive Waste (HLW) stored underground: “shallow” burial in mined repositories in crystalline rock, and deep geologic disposal in holes bored in crystalline or sedimentary rock, making use of metal canisters isolated from the rock by concrete or dense expansive clay. The present paper describes disposal in smectite clay for delaying or preventing radionuclides from reaching the biosphere when they can still cause great havoc. This is achieved by utilizing the great waste-isolating capacity of the expansive clay through its high hydrophilic capacity and large specific surface area, providing low porosity and limited interconnectivity of the voids, which both makes such clay low-permeable and operating with a very low through-diffusion rate of anionic species like iodine, and of some cationic radionuclides. The expandability of such clay means that it can swell and undergo self-healing in case of microstructural contraction caused by heating. The mechanisms involved in permeation and ion exchange are described based on conceptual microstructural models and their theoretical analogies. Stress/strain phenomena involved in saturation with fluids, desiccation, shearing under deviatoric conditions, and creep strain under stable conditions or at failure are described as well. Longevity matters are given limited space.