I learned a little about nuclear reactors in my time at Ontario Power Generation. I wasn't directly involved, so I'm not an expert.
However, I do know enough to know that the old Russian design that Chernobyl was built on was badly flawed, as were some of the early American designs.
Basically, they are unstable after a certain point - the coolant boils and nothing is left to cool the reactor. Cross that point and there is nothing left to do.
The CANDU (Canadian) reactor is one of the best in the world. It can extract more power from the same fuel than any other reactor design - you can even run one on spent Russian or American fuel, and the South Koreans have actually done this - taken spent Chinese nuclear waste (Russian reactor design) and used it as fuel! It also doesn't have that instability point as did the early American and Russian designs - the coolant will never boil away from the rods.
One idea that really intrigued me was from a private Chinese entrepreneur. He came up with a casing for fuel pellets that would only allow the radiation to escape if they were being bombarded. This means, basically, the fuel would work in a reactor, but as spend fuel it is almost completely inert. As a demo, he actually ran the reactor, then opened it and picked up one of the fuel balls. Plus, they are entirely scalable - since they don't need giant support buildings for cooling. The ball casing helps disperse the heat, and if the casing gets too hot it stops the reaction! Genius design. His demo reactor was about the size of a popcorn cart. If anyone knows the size of a modern nuclear plant, you know how amazing that is.