Immediately after being removed from the reactor, the spent fuel is stored in water tanks, in order to cool them enough to prevent the fuel rods from melting. A

Immediately after being removed from the reactor, the spent fuel is stored in water tanks, in order to cool them enough to prevent the fuel rods from melting. After a few years, however, the radioactivity has decayed enough that the fuel can be stored in "dry casks", essentially big concrete containers, with no water or otherwise active cooling necessary. A lot of commercial spent nuclear fuel is sitting around in such dry casks. They are expected to last 100 years or so; if we haven't figured out a better plan by then we can just shift the spent fuel into fresh dry casks.