Continuing the discussion from Why Sanders is still campaigning, in eight sentences:
I don’t know the exact percentages, but it’s quite low. There are reprocessing plants in England, France, Russia, India, and Japan. The US had one, since closed, and is currently building another.
The reasons it’s not in as wide use as it could be is mostly political and economic (by the obvious fact that it’s cheaper to use new fuel and store the spent fuel in the ground than it is to reprocess it) rather than technological.
Once you factor in all the externalities (e.g. if there was a political decision that spent fuel had to be reprocessed rather than stored), it would still be cheaper than continuing to use coal (the main externality of coal use is never factored in, i.e. the loss of everyone’s waterfront property).