This review describes nuclear waste forms for high-level waste (HLW), that is, glasses, ceramics, and glass-ceramics, as well as for low- and intermediate-level waste (LILW), that is, cement, bitumen, glass, glassy slags, and ceramics. Ceramic waste forms have the highest chemical durability and radiation resistance, and are recommended for HLW and actinide (ACT) immobilization. Most radiation-resistant materials are based on phases with a fluorite-related structure (cubic zirconia-based solid solutions, pyrochlore, zirconolite, murataite). Glass is also a suitable matrix for HLW containing fission and corrosion products, and process contaminants such as Na salts. Within the framework of the HLW partitioning concept providing separation of short-lived (Cs, Sr) and long-lived (rare earth element-ACT) fractions, glass may be used for immobilization of the Cs-Sr-bearing fraction, whereas the rare earth-ACT fraction may be incorporated in ceramics. Glass-based materials or clay-based ceramics are the most promising LILW forms, but cement and bitumen may also be applied as matrices for low-level wastes (LLW).