This review covers the corrosion interactions between different materials that are relevant to the disposal of high-level nuclear waste, in particular the waste forms and containers. The materials of interest are borosilicate glass, crystalline ceramics, metal alloys, and any corrosion products that might form. The available data show that these interactions depend on the structure, chemistry, thermodynamic history, and proximity of the materials in contact, as well as the environmental attributes, such as temperature, solution chemistry, and radiation. Several key mechanisms that govern these interactions are highlighted. Scientific gaps and open questions are summarized and discussed.