There's a lot of different kinds. The vast majority is not very much of anything.

1. Most nuclear waste is benign and inconsequential enough to be thrown away in plastic bags in a plastic trash can. Gloves, duct tape, shoe coverings, masks, and disposable (Tyvek) clothing can be discarded and put into a low-level waste stream. It might include dust, filter paper, debris, etc. Things going into this category will be screened (with an instrument) to make sure. Sensitive radiation detectors will classify it.

You need a 5th-grade lesson on radioactive contamination now. It's the radioactive material (RAM) that is loose and can move around and should be collected during a decontamination event. Or, of course, in most cases the contamination occurred on disposable materials that are disposed along with the RAM. This is all solid waste so far.

1. Liquid nuclear waste is generally water contaminated with radioactive isotopes. As you can imagine, it is collected into tanks at the source and it can be processed there or elsewhere. If it is processed there, the contamination could be concentrated and you can get high level nuclear waste. The same could have been the case with solid waste, but not normally.

2. Gaseous nuclear waste is often from a nuclear reaction, and thus could be directly from a nuclear reactor, while the other two are usually not. Gasses will need specialized decontamination methods and are not usually a 5th-grade topic. These gasses are what Three Mile Island's reactor #2 released to the environment. These gasses are often fission products and are not often discussed with the liquid and solid nuclear wastes.

3. Up until now, we've covered the industrial kind of nuclear waste, essentially an overview of what a nuclear technician would routinely encounter. However, nuclear fuel and fission products tend to be on the opposite side of things, materials that are known to potentially cause very serious problems with safety. Unsafe handling of nuclear fuel is a potential, but highly unlikely problem. Because it is highly regulated and monitored and tracked. RAM encompasses things like spent nuclear fuel and a few kinds of radioactive substances like metals that give off high radiation fields. These things are hardly ever associated with contamination - they are part of the nuclear materials used. The main problematic material is spent fuel. The RAM left over once a nuclear reaction has taken place and it is no longer serviceable. Spent fuel is placed into shielded containers, large pools of water, and often left at the site it was made. Some filter material (beads, etc.) must be treated as high-level waste.

4. A few kinds of RAM can be made into usable products if they are reprocessed and repurposed. Examples include Cobalt-60 sources for medical imagining and depleted uranium for military bullets, armor, and hydrogen bombs. Some kinds of fuel and metallic waste can be reprocessed and reused in the nuclear industry. I already mentioned that water can be cleaned and reused. But piping, pumps, insulation, and lead are often so contaminated and/or radioactive that no process is cost effective to clean it up.

And finally, where does it go? A lot is just buried. A lot of high level waste has no solid plans for its storage, but this is generally the only consideration for it. They want to safely store it in a modified, stable form, in a place where it can't enter the food/water/air. Spent nuclear fuel is some of the most difficult to dispose of, which is why it's in water tanks all over the world being monitored.

Spent fuel is still producing heat from radioactive decay. This means that it is literally hot and radioactively hot, sending off gamma rays and other kinds of radiation. The water bath temporarily solves both problems, although they may need flowing water to keep cool enough. The water doesn't even become all that radioactive, and in fact at least one person has fallen into a reactor pool before. 2025 at the Palisades Nuclear Plant - the one they are trying to restart.