We may discuss it further if we have time.
At the dawn of the nuclear age, a rather large number of types of reactors were believed to be possible. Tests relevant to these types of reactors were conducted, and in a few cases, reactors were built and tested.
Factors that played a role in decisions about what type of reactors were to be built depended on subtle issues, most notably access to uranium resources and more importantly enrichment technology. At the dawn of the nuclear age, the US had a monopoly on enrichment and more or less denied even allied nations, including Britain and Canada - though both sent scientists to the Manhattan project - access to it. Thus other nations wishing to develop nuclear power needed to rely on reactor designs that are non standard today. The Gen I reactors - pilot scale plants all, typically with full power ratings of less than 100 MW (about 1/10th as large as Gen II) reactors were not standardized and reflected the need to avoid enrichment.
There are two ways to avoid enrichment. One was the excellent design selected in Canada, the CANDU heavy water reactor - using deuterated water - that can run off of natural uranium because of its high neutron economy. The other way is to use a graphite moderated reactor - the Chernobyl type or a design that is similar. Moderation is the process of slowing neutrons down until their speed is about the equivalent of thermal (Maxwell-Boltzmann speeds) of ordinary molecules at a given temperature.
Gen I: The first industrial scale reactor was the B reactor had Hanford. It operated for more than 20 years, produced no electricity and ran to make plutonium. The first grid integrated power reactors were British and Soviet. The British design was the Magnox reactor, which used graphite moderation and a magnesium fuel that was easily treated chemically to recover plutonium. This plutonium was designed to be recovered for civilian and military purposes. The United States Navy designed reactors that proved able to go commercial for power generation but were originally designed for submarines: Pressurized Water Reactors. Here the water was both moderator and heat transfer agent. The heat was transferred to a steam generator that actually turned the turbines. The first electrical PWR was essentially a landlocked submarine reactor - Shippingport. A fourth type of reactor, the boiling water, reactor BWR, simply used steam directly produced in the core to drive the turbines.
All of these reactors were Gen I in that they were small and not really standardized in any way.
Gen II began with the development of larger scale BWR and PWR and a few other types of reactors, in particular Gen II CANDUs. These reactors form the bulk of the world's present day fleet and were built in the 1970's. While they have been mostly reliable, some have been balky, and many had variable designs that responded to particular company demands as well as publicly driven "safety" modifications that were produced in an ad hoc way, sending construction costs through the roof in some cases. This lead to unclear costing and delays. Nevertheless, with a few well known exceptions, the reactors worked very well and with experience, became highly reliable and profitable.
The lessons learned in the Gen II program were incorporated into Gen III, given cheaper and yet stronger "defense in depth" approaches to reactor design. The most notable features are passive safety features (some exist in Gen II systems) that shut down the reactor automatically during excursions, rely on fewer pumps, stronger materials, modular construction parts and ease of assembly and disassembly. These designs draw on decades of experience. Graphite moderation was abandoned.
Gen IIIB designs, some of which are now available, are designed to have flexible fuel loadings and can burn many types of fuels, including those that are thorium based, plutonium based and even based with higher actinides such as neptunium and americium.
Gen IV reactors are designed for missions that have become apparent over the last 50 years: The need to use nuclear power to make fluid fuels is one such mission, non-proliferation another, high temperature process heat, another, and the consumption of materials sometimes called "nuclear waste" is another.
This presentation shows the idea:
http://eurograd.physik.uni-tuebingen.de/ARCHIV/Vortrag/Zimmermann20060630.pdfSlide 44 is a graphic attached to the various generations and their time lines.
Slide 51 is designed to show that by fissioning the higher actinides and plutonium, spent fuel need be stored only got 500 years to be less toxic than the uranium that formed it. (In other words, the blue line and red line material are burned to recover energy) and the long term radiotoxicity is eliminated.
Many other slides give details of nuclear engineering approaches.
Let me know if I can answer additional questions you may have.