I know of one cool idea of how to do this … By using the neutrons produced by a fusion reactor, we could ‘burn up’ the long-lived radioactive waste produced by a fission reactor. They would still be a bit radioactive but would be safe in a much shorter time. This could also be used to generate electricity in what is called a ‘fusion fission hybrid’. China are interested in building one of these reactors to see how possible it is 🙂
Jack has effectively given you the answer. The chemistry my group has developed means that it is now possible to separate out the long-lived nasties in waste nuclear fuel – the so-called minor actinides, americium, curium and neptunium and these can be placed in the Generation IV reactor Jack mentioned and destroyed, being turned into non-radioactive materials. This is actually a much cheaper (and safer) way of dealing with the waste than just burying it, which is what had been proposed until now. We simply do not know what will happen to the waste or where we store it over millions and millions of years. We have been very irresponsible in the past. There are currently about 200,000 tonnes of untreated waste nuclear fuel being stored around the world.