So how are we currently dealing with all this nuclear waste?  There are many ways.  The above video from the Last Week Tonight television show discusses some methods, and here is another overview.  However a lot depends on the nature of the waste and state/federal regulations.  Some waste is stored in cooling ponds on site, some is put into large containers and buried, in the past some was dumped in the ocean -- and the list goes on.  In nearly all of those cases, the waste is treated as whole, without regard to what's actually in the waste itself.  However, many feel that high-level (highly radioactive) radioactive waste (including strontium and cesium) should be separated from low-level radioactive waste (like rare earth elements and other less toxic substances) so that waste can be stored more efficiently, or even recycled.  Since we don't have a permanent storage facility for nuclear waste in the United States, it is imperative that the most dangerous aspects of the waste are treated so they do not enter the environment and become biologically available
To tackle this problem, I turn to an important class of minerals that have been explored for waste storage in the past.  These are the naturally occurring zeolites and related microporous minerals.  These minerals act like natural molecular sponges; they are porous on the molecular scale (microporous), and can absorb elements from a liquid into the solid crystal.   This process occurs spontaneously in nature, and has likely been going on for billions of years.  When these microporous materials start to absorb the element from the liquid, they also have to release back into the liquid, an element that already resides in the crystal.  It's an exchange process.  Think of a dish sponge that has been colored green by food dye.  If you want to wash off the green dye, you have to replace the dye with fresh water.