It's not that hard conceptually to deal with. Ideally you reprocess it into more fuel. Worst case you store it on-site in casks, or bury it somewhere geologically stable.
It may not be hard conceptually, but it does seem hard practically. To date, the number of geologically stable sites used for commercial - as opposed to experimental - storage of nuclear waste appears to be zero.
We could also drop it to the bottom of the ocean, as we did for decades. Any spillage will dilute heavily (there's already plenty of radioisotopes in seawater), and it will take quite a while until geological processes get the bottom of the ocean to surface.
Of course, we don't do that anymore, because it's stupid: nuclear waste is too valuable to just dispose of it like that.
