The basic principles of incorporating high level radioactive waste into glasses, ceramics and glass composite materials (GCMs) are described. Current UK technology uses glass wasteforms for the products of reprocessing while some waste streams may be incorporated in ceramics and difficult or legacy wastes will require the development of other wasteforms many of which will be GCMs. Processingproperty- structure relations in novel wasteforms are described including the use of self-sustaining reactions to produce a composite ceramic wasteform based on TiC and Al2O3 from irradiated graphite and development of a GCM wasteform for immobilising spent zeolite sand filters.