"High level Waste (HLW) arises from the use of uranium fuel in a nuclear reactor and nuclear weapons processing. It contains the fission products and transuranic elements generated in the reactor core. It is highly radioactive and hot. It can be considered the "ash" from "burning" uranium. HLW accounts for over 95% of the total radioactivity produced in the process of nuclear electricity generation.

There have been proposals for reactors that consume nuclear waste and transmute it to other, less-harmful nuclear waste. In particular, the Integral Fast Reactor was a proposed nuclear reactor with a nuclear fuel cycle that produced no transuranic waste; in fact, it could consume transuranic waste. It proceeded as far as large-scale tests but was then cancelled by the US Government.

To solve the waste disposal problem, the IFR had an on-site electrowinning fuel reprocessing unit that recycled the uranium and all the transuranics (not just plutonium) via electroplating, leaving just short half-life fission products in the waste. Some of these fission products could later be separated for industrial or medical uses and the rest sent to a waste repository (where they would not have to be stored for anywhere near as long as wastes containing long half-life transuranics). It is thought that it would not be possible to divert fuel from this reactor to make bombs, as several of the transuranics spontaneously fission so rapidly that any assembly would melt before it could be completed. The project was canceled in 1994, at the behest of then-Secretary of Energy Hazel O'Leary."

from the IFR site:

"Fuel recycling greatly reduces the amount of the radioactive wastes that must be buried in geologic repositories. After 300 to 400 years, IFR waste - the products of fissioning - are as safe as the natural ore the fuel came from. "

i think most transuranics (elements beyond uranium) have very long-half lives (100kyrs+).  they can still emit quite a bit (high radiation flux) but the transitions can have very long decay times.   perhaps the transuranics and actinides are not as "hot" as the short half-life (<300yr) fission products, but they are still hot enough to be a serious health and environmental problem.  

you're right about the thorium, they are using that for some breeders/burners as well.