High-level nuclear wastes (HLW) are the liquid effluents that result from the reprocessing of spent nuclear fuel. These wastes are typically solidified in a glass for final disposal in deep geologic formations. At present, there is no geologic repository receiving these vitrified wastes. A primary issue in nuclear waste management is whether there can be societal, regulatory, and political confidence that the radiotoxic constituents of HLW can be safely disposed of for hundreds of thousands of years. If a glass waste form, placed at a depth of hundreds of meters, is stable and essentially insoluble in groundwater, it would be almost impossible for radioactivity to reach the environment. This paper summarizes the state of knowledge of glass performance in a geologic repository and examines the question of whether the long-term stability of the glass and radionuclide retention can be assured.