As far as I know (pretty low bar)
We have yet to safely dispose of a single once of nuclear wast.
Those waste facilities we haphazardly created are decaying rapidly for which I have yet to hear a single solution.
<IFF> we pursue nuclear power through fission, we really should pursue thorium molten salt reactors, IMO. There has been a lot of research done on them, especially in the last decade or so. If you want to learn more about them, I'd recommend starting with the Oak Ridge National Laboratory Molten-Salt Experiment.
Thorium MSRs were the original direction the US wanted to go with nuclear reactors because of their inherent safety factor (the design of an MSR makes it PASSIVELY safe; if ANYTHING goes wrong with the reactor, it just stops, in addition you can't easily use a Thorium reactor to breed things like Plutonium). The reason the US didn't go that path back in the 50s was because the DoD wanted Plutonium for weapons, which requires a breeder reactor; in other words NOT Thorium.
In addition, Thorium reactors can 'eat' all of the waste from older reactors. While Thorium reactors DO produce some very high-level waste, this is actually a good thing; it means that the waste decays to safe levels within a few decades, rather than a few millennia, and there is SUBSTANTIALLY less of it, making storage easier. Further, the small amount of highly radioactive waste that is produced is actually TOO radioactive to make a viable weapon from (I'm talking like a bomb; there are obviously OTHER ways that a person intent on mayhem could take advantage of highly radioactive nuclear waste, but those other ways apply to a large amount of other poisonous materials as well, so again it is a manageable problem).
The big problem holding Thorium MSRs back right now is that the regulatory regime in the US is so nightmarishly convoluted and so stuck in the 1970s that getting a new reactor type qualified for use is nigh impossible.
With respect to waste, we should also objectively discuss some things about radioactivity.
In general, I'm not concerned about waste that takes 10,000 years or longer to decay. Do you know why it takes that long? Because it's only BARELY radioactive!!!
Waste that decays in weeks to months is HIGHLY radioactive; that's why it decays so fast. That's commonly referred to as HLW, or high-level waste. Store this for a few decades and it is essentially inert.
Even most MLW (medium-level waste) is only hazardous for a couple of hundred years at most. IMO, this is the stuff we probably should be MOST concerned about, as it generally has rather high levels of radioactivity and hangs around for a while (on human timescales). Still, this problem should be manageable, if we really want to do so.
There are a lot more details and nuance than I have gone into here. It is frustratingly difficult to find detailed and accurate information with which to assess the risks, because it's all surrounded by political grand-standing (both for and against). Obviously, a rational person in such an environment is going to choose the least risky option, but how exactly do you evaluate that, when one side of the conversation is sowing FUD as fast as they can, and the other side of the conversation is trying to white-wash everything? The political environment is so toxic that anyone who tries to approach the subject objectively seems to either risk being labeled as a corporate shill or having their research funding pulled, or even both.
All of the above might actually be moot, though. We seem to finally be making some progress on battery technologies that will be able to displace Lithium Ion, and be economical enough to be useful as grid storage. If we can crack that nut, we can start storing the excess solar and wind power we are generating and making better use of it. Once that happens, conversations about nuclear (fission OR fusion) no longer make sense except for very specific applications. I think we can all agree that such an outcome is probably the most desirable.