Storage of long lived nuclear waste is often considered a major problem. There are suggestions of firing them to the sun (worst idea ever), burring them in subduction zones (a bit more sensible) or in special sites with plenty of warning for future generations (artists get creative on this one).

The thing is, nuclear waste may actually be among the most valuable things on earth. These elements do not exist in nature, and producing them require nuclear reactors and enriched uranium, which is a finite resource.

Even today we have the technology to burn nuclear waste in fast breeder reactors, though for some reason we haven't made a lot of progress, maybe it is not commercially viable compared to more conventional reactors. This has the potential to supply us with energy for so long that we can effectively consider it renewable energy.

All that to say that in the future, nuclear "waste" may become extremely valuable. I find one particularly ironic quote from a suggested warning message for long term nuclear waste storage sites. "This place is not a place of honor... no highly esteemed deed is commemorated here... nothing valued is here." I find it extremely dismissive of future humanity, as if we somehow reach the peak of technological progress and that future generations will be cavemen.