The predominant technology used to generate civilian nuclear power today, yesterday, and ever since we've had "nuclear power" is the the Light Water Reactor (LWR). The LWR's co-inventor had this to say, many years after filing his 1947 patent:
"One publicist claimed that the light-water reactor had been chosen after long and careful analysis because it possessed unique safety features. I knew this was untrue: pressurized water had been chosen to power submarines because such reactors are compact and simple. Their advent on land was entirely due to Rickover's dominance in reactor development the 1950s, and once established, the light-water reactor could not be displaced by a competing reactor. To claim that light-water reactors were chosen because of their superior safety belied an ignorance of how the technology had actually evolved... the Army finally decided that even small light-water reactors were too difficult and costly to maintain, and they were all eventually decommissioned." ‑ Alvin Weinberg ("The Second Nuclear Era", 1994)
The LWR is the QWERTY keyboard's counterpart in reactor design – not optimal, yet the industry norm. Few today remember the alternate approach that was once actively investigated, the Thorium Molten Salt Reactor (Th-MSR). Today Thorium Molten Salt Reactor is frequently referred to as Liquid Fluoride Thorium Reactor (LFTR, pronounced "lifter").
For a detailed analysis of exactly why this technology has been overlooked, please watch Kirk Sorensen's presentation to Google on the subject.
A: Thorium is a naturally-occuring mineral that holds large amounts of releasable nuclear energy, similar to uranium. This nuclear energy can be released in a special nuclear reactor designed to use thorium. Thorium is special because it is easier to extract this energy completely than uranium due to some of the chemical and nuclear properties of thorium.
A: A liquid-fluoride nuclear reactor is different than conventional nuclear reactors that use solid fuel elements. A liquid-fluoride reactor uses a solution of several fluoride salts, typically lithium fluoride, beryllium fluoride, and uranium tetrafluoride, as its basic nuclear fuel. The fluoride salts have a number of advantages over solid fuels. They are impervious to radiation damage, they can be chemically processed in the form that they are in, and they have a high capacity to hold thermal energy (heat). Additional nuclear fuel can be added or withdrawn from the salt solution during normal operation.
A: Very safe. Unlike other coolants considered for high-performance reactors (like liquid sodium) the salts will not react dangerously with air or water. This is because they are already in their most stable chemical form. Their properties do not change even under intense radiation, unlike all solid forms of nuclear fuel.
A: So-called "nuclear waste" or spent-nuclear fuel is produced in conventional (solid-core) nuclear reactors because they are unable to extract all of the nuclear energy from their fuel before they have to shutdown. LFTR addresses this issue by using a form of nuclear fuel (liquid-fluoride salts of thorium) that allow complete extraction of nuclear energy from the fuel.