The Nuclear reactors that are currently in use in the United States are obsolete. They require enriched uranium as their sole input, use less than 1% of the energy content, and leave highly radioactive partially used nuclear fuel that they aren't designed to consume fully.
Continuing to build and operate these outdated reactor designs isn't sustainable. At the current rate, it would turn all of the world's easily accessible uranium into "spent fuel" and "depleted uranium" in less than 100 years.
Modern designs are better. The Integral Fast Reactor, a research reactor that operated until 1994, is designed to use about 99.5% of the energy content of nuclear fuel through continuous on-site reprocessing. That means that it actually consumes for power both the "spent fuel" and the "depleted uranium" that present-day designs produce as waste.
The IFR, and other similar designs, are also capable of using the "spent fuel" from our current plants. This means it's not waste, it's just fuel we can't use right now. Once these modern plants are built, the "spent fuel" storage problem will mostly go away.
The IFR program was canceled in 1994, probably due to lack of public support for nuclear power research. The fully functional experimental reactor that had solved the nuclear waste problem and the fuel supply problem was shut down. Until very recently, research into nuclear power technology had slowed drastically.
As an alternative to putting this existing modern technology into production and using the remaining energy capacity of the "spent fuel" from current reactors (around 98% of the energy), some suggest that we encase it in glass to make it hard to get at and then bury it in the mountains. This is usable nuclear fuel - throwing it away is ridiculous idiocy, especially since in it's current form it will stay highly radioactive for tens of thousands of years.
Other people suggest that the spent fuel be chemically treated to prevent the plutonium from being recovered due to proliferation concerns. That's an excellent way to produce high volumes of nuclear waste that really can't be used as fuel, and really will stay highly radioactive for tens of thousands of years. In a proper fuel cycle, recovering weapons grade plutonium is near-impossible anyway - there's no need to turn useful fuel into dangerous unusable waste to prevent it.
Modern reactors need to start getting built. Proper fuel cycles that don't produce large volumes of partially-used fuel as byproducts need to be mandated for new reactors. Existing partially-used fuel needs to be stored, so it can be used in these new reactors.
Research needs to continue, and more efficient and more proliferation resistant designs need to be developed and shared. Any other plan leaves us with obnoxious unsolved problems