The basic principles of incorporating high level radioactive waste into glasses, ceramics (Synroc type) and glass composites including glass ceramics are described. Current UK technology uses glass wasteforms for the products of reprocessing, although many countries are temporarily storing the ceramic spent fuel for eventual disposal. Some waste streams may be incorporated into ceramics, but difficult or legacy wastes will require the development of other wasteforms comprising composite systems of crystals and glass. The importance of processing-propertystructure (especially durability) relations in such systems over size scales from the atomic to the geological and on timescales to hundreds of thousands of years is highlighted.