Sherman, set the way-way-back machine - 2 billion years ago or so...
About two billion years ago, there were spots on the Earth's crust where the density and amount of fissile uranium was large enough that it was capable of having sustained fission reaction. Originally scattered about the crust in parts per million, about 3 billion years ago the Earth's atmosphere became one where oxygen dominated it allowing uranium oxide to be dissolved out of the rocks into water ways. The water slowed down in ancient swamps and river deltas and deposited sediments and the uranium perticipated out over a rather thin layer of low concentration. Over time, the uranium layer was pushed further down by crustal movements and rainwater. This eventually caused globs of uranium in rather high concentrations to form that ranged from a few inches across to the size of a large car.
Having enough mass, each glob could now become a fission reactor. Along with enough mass, three things where needed for a natural reactor - a rather high concentration of uranium, few neutron absorbers (things like carbon and sandstone), and a high concentration of a moderator (water in this case).
About 2 billion years ago, the ratio of 235U to 238U was about 3% - a similar ratio to that which is in 'enriched uranium' needed for man made fission reactors. Today, that ratio in nature is about 0.7%.
About 2 billion years have passed since the last reactor 'ran'. The waste products have decayed away (even those with half lives in the millions of years). The only 'clocks' left are those of the billion year clocks - U238, Rb87, and Sm147
Now, fast forward back to today... or close enough to today when talking about a billion years - 1972. In the OKLO uranium deposit (in the country of Gabon in equatorial Africa) , several of these ancient fission reactors where discovered. This was considered in 1956 by a Japanese physicist named Paul Kuroda, who wrote down the requirements for a natural reactor. On June 2, 1972 a French analyst working at the Pierrelatte nuclear fuel processing plant noticed that the ratio of the 235U/238U had a small change (0.00717 compared to 0.00720). This small change in a ratio indicated that something had happened in the past. Initially it was thought that some of the nuclear waste had somehow gotten back into the processing plant, but this was quickly ruled out. Other suggestions included spent fuel dumped from a UFO or an ancient nuclear war site. Tracking the fuel back to its source it was discovered that the mine in South West Africa was its source and had a very high concentration of uranium. Furthermore, it was discovered that there were large amounts of ancient fission product waste embedded in the ore.
Fossil reactors give scientists the opportunity to look at the stability of the fundamental constants of the universe
(has the speed of light changed?) across cosmological time scales along with the opportunity to look at what nuclear waste does millions or billions of years from now.
The OKLO fossil reactors demonstrate the 'multiple barrier' that is used today in radioactive waste disposal which has the waste in the center as part of a chemically and thermally stable mineral which is then encased in a ferrous container, that is encased in a porous media which is encased in a low porous media that is in a geographical stable part of the tectonic plate. This way, even if the waste somehow escapes the ferrous container it is captured in the outer containers.
Today, the fossil reactor looks like some yellow rock embedded in quartz (the sandstone that acted as a moderator for the reactor became quartz when it melted). Fifteen reactors were discovered at the OKLO site, some of them are still intact, others have been completely mined out and only samples remain.
http://antwrp.gsfc.nasa.gov/apod/ap021016.html
http://www.curtin.edu.au/curtin/centre/waisrc/OKLO/