I would also encourage other's to click on acidburnNSA's profile as this is where their expertise lies and they have written extensively (with plenty of links) on the subject.[0]
We have no permanent disposal facilities, not even in the planning stage.
https://www.gao.gov/key_issues/disposal_of_highlevel_nuclear...
https://en.m.wikipedia.org/wiki/Yucca_Mountain_nuclear_waste...
The anti-waste-disposal crowd in the environmental movement feels exceedingly disingenuous.
The amount of goal post moving they've engaged in over the decades makes it clear that their actual goals are to prevent any waste disposal site from being constructed, rather than specific, actionable complaints.
Which is insane, from a net-benefit perspective, as the alternative is to leave nuclear waste dispersed around the country, closer to population centers.
It's a matter of political will at this point.
"Ensuring access to dedicated funding – Current federal budget rules and laws make it impossible for the nuclear waste program to have assured access to the fees being collected from nuclear utilities and ratepayers to finance the commercial share of the waste program’s expenses.
We have recommended a partial remedy that should be implemented promptly by the Administration, working with the relevant congressional committees and the Congressional Budget Office. A long-term remedy requires legislation to provide access to the Nuclear Waste Fund and fees independent of the annual appropriations process but subject to rigorous independent financial and managerial oversight."
[1] https://web.archive.org/web/20120807061024/http://brc.gov/si...
Nuclear waste is radioactive, but not so radioactive that it's unsafe to stand next to a container. Most waste is stored on site.
It actually doesn't make sense to move nuclear waste to permanent storage because some reactor designs can use this waste as fuel.
People use "what about the waste" as a reason to not use nuclear. Yet, fossil and renewable biofuel waste is (as mentioned) just dumped into the biosphere where it ends and estimated 8 million lives early per year, according to the WHO.
https://www.who.int/health-topics/air-pollution