During the past 70 years, more than 2000 metric tonnes of Pu, and substantial quantities of the `minor' actinides such as Np, Am and Cm, have been generated in nuclear reactors. Some of these transuranium elements can be a source of energy in fission reactions (e.g. 239Pu), a source of fissile material for nuclear weapons (e.g. 239Pu and 237Np), and of environmental concern because of their long half-lives and radiotoxicity (e.g. 239Pu and 237Np). There are two basic strategies for the disposition of these transuranium elements: (1) to `burn' or fission the actinides using nuclear reactors or accelerators; (2) to dispose of the actinides directly as spent nuclear fuel or to `sequester' the actinides in chemically durable, radiation-resistant materials that are also suitable for geological disposal. For the latter strategy, there has been substantial interest in the use of actinide-bearing minerals, especially isometric pyrochlore, A2B2O7 (A = rare earths; B = Ti, Zr, Sn, Hf), for the immobilization of actinides, particularly plutonium, both as inert matrix fuels and nuclear waste forms. Systematic studies of rare-earth pyrochlores have led to the discovery that certain compositions (B = Zr, Hf) are stable to very high doses of α-decay event damage. Recent developments in the understanding of the properties of actinide-bearing solids have opened up new possibilities for the design of advanced nuclear materials that can be used as fuels and waste forms. As an example, the amount of radiation damage that accumulates over time can be controlled by the selection of an appropriate composition for the pyrochlore and a consideration of the thermal environment of disposal. In the case of deep borehole disposal (3–5 km), the natural geothermal gradient may provide enough heat to reduce the amount of accumulated radiation damage by thermal annealing.