To make this situation a bit more manageable, Hitachi, in partnership with MIT, the University of Michigan, and the University of California, Berkeley, is working on new reactor designs that use transuranic nuclear waste for fuel; leaving behind only short-lived radioactive elements.
In popular imagination, nuclear waste is a wildly radioactive goo that glows like the back end of a lightning bug. But in real life, the real problem of nuclear waste isn't the "hot" stuff, but the mildly radioactive elements with atomic numbers greater than 92. That's because highly radioactive elements have short half lives. That is, they burn themselves out very quickly – sometimes in a matter of minutes or even seconds.
On the other hand, mildly radioactive elements, such as plutonium, have half lives measured in tens of thousands or even millions of years. That makes storing them a very long-term problem, and is a particular difficulty in countries like the United States that don't recycle transuranium elements by fuel reprocessing or fast-breeder reactors.