On this subject I have some expertise...
having worked the past 25+ years at DOE operated nuclear facilities. I am not a scientist, I am not a physicist, I am an Operator. I operate the equipment and do the hands on work. I can't do the calculations to design a reactor or a fuel reprocessing plant, but I could build one that worked, (provided the materials) from what I have learned and done over the years.
As others have said, what the public "knows" about nuclear power and nuclear waste is mostly wrong. This comes from nearly half a century of Hollywood bull****, and agenda driven individuals making a point of telling only part of the truth. If there is anything in the world that has gotten more bad press than legal gun ownership, it is nuclear energy.
First, some terms; Fission - splitting atoms (uranium/plutonium) is the power of nuclear reactors and atomic bombs. Fusion -fusing light atoms together (hydrogen) is the power of the sun, and the H-bomb. We can create a fusion reaction, but we cannot yet control one. A bomb yes. A reactor, no. When we can control a fusion reaction, our energy problems will be solved for as long as matter exists in the universe, but until then, other things must do.
One thing the public does not well understand is that "radioactive" does not automatically mean lethal or even dangerous. There are many naturally occurring radioactive isotopes, some of them are found in every living thing. It is the amount that makes the difference. Sort of like you need iron in your blood in order to live, but if I drop a 10,000lb ingot on your head it won't be very good for you. Sort of.
The waste from a nuclear reactor comes in three general categories. Low level waste - all the contaminated material generated by operating the plant (gloves, tape, filters, protective clothing, tools, and contaminated equipment) These kinds of items have detectable levels of radioactive contamination, which would only be harmful if ingested, long term.
High level waste - which is material that does give off damaging levels of radiation -pipes and pumps from primary coolant loop, the coolant water, (depending on design) itself and of course, the spent fuel.
The third category is waste that contains radioactive material AND hazardous chemicals. Each type is handled differently. The spent fuel is the most difficult to store, and remains lethally dangerous for a long, long time, but not quite what everyone seems to think. Physically, more than 90% of the spent fuel remains relatively harmless Uranium. The high dose rate emitters (Cs & Sr) will continue to be dangerous for decades, up to a couple of centuries, but only if you keep them in your back pocket. The further away you are, the weaker the dose, due to the inverse square law. 2 feet away is 1/4 the contact dose. 3ft, 1/9th, etc.
I can discuss this subject at length, and in great detail, from a blue collar point of view. Anyone interested, PM me.
The way to permanently handle the "waste problem" of nuclear power is not to bury it in the ground (that is only temporary), but to shoot it into the sun. Don't use rockets, use mass driver (rail gun) technology. Turn it into glass first (after removing all reusable elements), so it cannot get into the environment, and then launch it. With current technology you could build a facitlity up the side of a mountain, and launch a telephone pole size payload out of orbit (no possibility or returning to earth) every few minutes, using only electricity, from now on, until the energy death of the universe. If you wonder why no one has (or is) doing that, follow the money. Yes, it really is that simple.
Yucca Mountain was supposed to be finished a decade ago, and won't be ready they say for another 10-12 years. AND, according to some calculations
won't be big enough for the waste that they are already committed to store, let alone what we are still producing.
FYI: How many of you folks know that the Soviet Union funneled a lot of money into the US & International anti nuclear movements, up until the end of the Cold War.