The reprocessing of nuclear spent fuel generates highly radioactive liquid wastes (HLW) that must be isolated from the biosphere in very durable solid matrices. In the first part of this book, generalities are presented on the radionuclides occurring in HLW and on the main characteristics and preparation methods of waste forms (glasses, ceramics, glass-ceramics) for the immobilization of separated or non-separated wastes. In the second part, the characteristics of two categories of long-lived radionuclides (135Cs and minor actinides Np, Am, Cm) and the main matrices proposed for their specific immobilization are reviewed. Results are also presented on ceramic and glass-ceramic matrices developed for the conditioning of Cs (hollandite) and minor actinides (zirconolite, zirconolite-based glass-ceramic, apatite-based glass-ceramic) and studied in the authors' laboratory. The last part of this book concerns glassy waste forms used or envisaged to immobilize non-separated highly radioactive waste solutions arising from nuclear spent fuel reprocessing. Generalities about the structure and the properties of silicate, borate and borosilicate glasses are presented before developing how fission products and actinides can enter the structure of nuclear glasses. The relation that may exist between nuclear glasses composition, structure and crystallization tendency during melt cooling is illustrated by results obtained in the laboratory of the authors on non-radioactive borosilicate nuclear glasses envisaged to immobilize Mo-rich and rare-earth-rich highly radioactive solutions.