Please check out some up-to-date information about nuclear waste storage. We've gotten to the point refinement has taken reactant levels down to acceptable levels for low-risk storage and can even re-use them in other reactor designs.
So, it looks like re-processing other then for weapon production only gets done on a very small, experimental scale because it is simply not economical, (https://en.wikipedia.org/wiki/Nuclear_reprocessing). This still leaves us with an endlessly growing stockpile of dangerous nuclear waste products.
Any specific sources of up-to-date information you recommend?
In two decades we’ll be sending nuclear waste into deep space.