In what part of a nuclear power plant does nuclear fission take place?

Answer 1

The controlled nuclear reaction takes place in the "core", which for the type of plant can mean a few different things. The core is made up of the fuel, supporting structure, and a moderator.

In the United States all plants are of two types (Boiling Water Reactors and Pressurized Water Reactors), both of which use a pressure vessel filled with water to contain the core. The pressure vessel is then places inside a steel and concrete containment structure, which from the outside looks like a cylindrical building, a dome, or a large cube. The containment structure is designed to prevent the release of radioactive material to the environment in the case of a "worst case scenario" accident.

In Canada the core is contained within a much larger structure known as the calandria, which is then inside a similar containment to the U.S. style. Reactors in Europe are much like those in the United States, except for eastern Europe (the former Soviet bloc). In all cases there are multiple layers of containment between the radioactive fuel and the environment.

Answer 2

It takes place in the reactor core in the fuel rods.