An overview is given of the immobilization of high level radioactive waste (HLW) and surplus materials from a variety of commercial and defence sources employing glass and ceramic hosts. A number of specific host materials are reviewed, including borosilicate and phosphate glasses, glass-ceramics and crystalline ceramics. Topics covered include wasteform processing and manufacture, in addition to wasteform stability, durability and mechanical behaviour. Although, at the present time, borosilicate glass is the generally accepted first generation wasteform for the immobilization of HLW, the emergence of new sources of radioactive materials requiring immobilization has renewed interest in many of the alternative candidates. These include, in particular, titanate, zirconate and phosphate based ceramics, together with iron phosphate based glasses and basaltic glass-ceramics. The relative merits and limitations of each host material are compared and discussed, with particular reference to processing considerations and to current and likely future requirements.