The heat of the fission reaction is removed by the water, which also acts to moderate the neutron reactions. An alternative form of nuclear fuel would be fissile uranium-233 (U-233) made by the neutron-bombardment of the common thorium-232. Also, fissile uranium-234 (U-234) is found as a trace addition to U-235 wherever U-235 is found. They are both good nuclear "fuels".
One type uses solid graphite for the neutron moderator and ordinary water for the coolant. See the Soviet-made RBMK nuclear-power reactor. These were the reactors that were the cause of the Chernobyl disaster.
In a so-called advanced gas-cooled reactor, a British design, the core is made of a graphite neutron moderator where the fuel assemblies are located. Carbon dioxide gas acts as a coolant and it circulates through the graphite removing heat.
Several merely experimental or hypothetical nuclear reactor cores are mentioned below.
There have been developmental graphite-moderated nuclear power reactors that were cooled by helium gas. These are no longer in service.
The core of a molten salt reactor is a block of graphite through which holes are bored in which molten salt circulates. The graphite serves as a neutron moderator, it is the solid structure of the reactor. The molten salt that circulates in the channels is both the fuel and the coolant, it contains the fissionable material needed to sustain the chain reaction.
A set of compact nuclear reactors were developed by the United States under the Systems Nuclear Auxiliary Power Program (SNAP). One SNAP reactor, the SNAP-10A was launched into space and was successfully operated for 43 days in 1965.
Aqueous homogeneous reactors cores employ water in which soluble nuclear salts (usually uranyl sulfate or uranyl nitrate) have been dissolved. As the water serves as the solvent for the uranium salts, it serves as the fuel. As it is water, it serves to cool the reactor as well- hence the name 'homogeneous' (as coolant and fuel are one homogeneous substance). The water can be either heavy water or ordinary light water.