According to the IAEA requirements, the liquid high-level radioactive wastes (HLW) of weapon plutonium production and spent nuclear fuel reprocessing are to be transformed to a solid form. For this purpose, alumophosphate glass is used in Russia, and borosilicate glass is used in all other countries. The highly efficient technology of HLW incorporation into glasses is available due to the low melting temperature of these glasses, minimizing radionuclide volatilization and power consumption. These glasses are rather highly soluble in aqueous solutions and tend to recrystallize. The immobilization of actinide-bearing wastes requires safer matrices providing isolation of the waste for many thousands of years. The crystalline matrices where radionuclides are bound in crystal lattices are the best candidates in this respect. This paper contains a review of published data on borosilicate glasses and covers the results of the study of alumophosphate glasses performed at IGEM RAS. The Synroc ceramics synthesized from the same starting material by the hot pressing technique in Australia and by inductive melting in a cold crucible in SIA Radon were compared. The latter ceramic materials are composed of mineral grains with larger sizes, include pores (up to 5 vol %), are free of metal alloys, and do contain molybdates of alkali or alkali earth elements. The formation of molybdates is caused by higher oxic conditions of synthesis. When interacting with aqueous solutions, the melted ceramics confine actinides securely and Cs and Sr poorly due to the high solubility of molybdates. Zirconolite ceramics with high concentrations of elements simulating radionuclides were also produced and investigated. The distribution of different elements among the phases of ceramics was studied in detail. It was concluded that the melted zirconolite materials are suitable for conservation of the actinide portion of HLW after its fractionation. The fractionation technology is being promoted now at the radiochemical plant of the Mayak Production Association (PA Mayak) (Glagolenko et al., 1996; Dzekun et al., 1996).