Waste never disappear, it just get transformed in something else.

Paper? Can be recycled to be more paper or burned to be ashes and gas

Radioactive waste? Eventually it became lead, just in a long time, anyway, this was just to make you know that waste don't "disappear" like magic.

Radioactive waste can be repurposed, at least, for the majority of it, in the other cases where it can't be repurposed they try to get as much as they can from the waste(making it also less risky to manage overall) and enclosed in a reinforced concrete cage in a earthquake-safe area, in something like 50~ years it became almosts safe and can be managed again