Thank you YoungTurk, I am happy that you found my post helpful.
Reprocessing. A really vast subject.
Nuclear reactors are very inefficient and use a relatively small percentage of the fissile fuel. Moreover U238 captures neutrons, becoming Pu239 (there is a decay chain in between obviously), thus creating new fissile material.
So if you started with Uranium Oxyde enriched at 4% (pretty standard, but note that the enrichment varies by plant and position within the core), that is, 4% U235 and 96% U238 (oxydes), you would end up with something like 1% U235, 1% Pu239 and 240, 3% fission products (the "waste") and the rest still U238.
The bottomline is that we can take the spent fuel, reprocess it to extract the fissile material (U235, Pu239 and 241 mainly), add some more U235 and put it back as fuel in a reactor. This way you get the MOX fuel (Mixed OXyde) to use again in your plants. This is what the Japanese, Russians and French do.
Looking at the numbers above it sounds like a pretty good idea, by reprocessing we avoid wasting fuel. The problem with reprocessing is that you have to deal with a radioactive liquid in your reprocessing plant... very messy and expensive.
Moreover, while enriched Uranium's radioactivity is negligible, MOX fuel is quite radioactive (Am231, a deacay product of Pu241 is the main culprit) so the fuel fabrication needs to be automated in large part, raising the costs.
The bottomline is that, while reprocessing reduced greatly the volume of "waste" (from 100% of the spent fuel to, ideally, 3%), it is really too expensive, as of today.
And I did not even touch the proliferation risk.
This should answer to the first part of your question. To answer the second part, you could "seed" the fuel with Th232 so that, while the U235 gets "consumed" by fission, the Th captures neutrons transforming into U233 and effectively adding fissile material back.
Great, right? It sounds a lot like a free lunch, so there must be a problem somewhere. The problem is that the Th captures neutrons, thus changing the neutronic balance within the reactor. You would have to increase the initial enrichment of your fuel to generate enough neutrons to both sustain the chain reaction and provide neutrons to the Th.
There is also a problem that you can't optimize the reactor both for optimal capture and chain reaction, but that would require a longer discussion.
Having said that, the French and the Russians have experimented with a similar idea in their "fast" reactors. They put a "blanket" of fissionable material around the core(they used U238), that, capturing neutrons would become fissile (Pu, in this case).
This blanket would contribute very little to the energy produced, but would be periodically taken out, reprocessed to extract fissile material that would be fabricated into new fuel and put back in for the next cycle.
SuperPhenix, thanks to this configuration, achieved breeding ratios of 1.2,IIRC, that is, for every atom of fissile material you put in, you would get back 1.2 after reprocessing. This apparently puzzling result is achieved by converting useless U238 into fissile material (U238 is not fissile).
This method described here is what I was talking about when I meantioned in my earlier post that you can effectively multiply (in theory) your fissile Uranium reserves by a factor 40.
The reason why we don't do that? Uranium is (relatively)cheap and fast breeder reactors are even more expensive than the already very expensive thermal (classical) nuclear reactors.
But if we have to, we already have the technology to do all of the above.
NOTE 1: The neutronic behavior of the MOX fuel is different than normal UO2 fuel. Many of the modern thermal reactors can handle both, though.
NOTE 2: "Fast" reactors are reactos that work with a neutron energy spectrum centered on higher energy (Faster neutrons!) that normal "thermal" reactors ("slow" neutrons).
Most of the reactors today are thermal reactors. The Russians are still running their fast breeder reactor (BN-600), while the French have shut down theirs (Phenix and SuperPhoenix) because of the high costs and operational problems.
Look up SuperPhenix, it has been one of the grandest engineering projects in the last century (albeit not very successful)
NOTE 3: take a look at this report we did at MIT a while ago. Among the other things, you will find a discussion on once-through versus closed-cycle.