There are several types of nuclear reactors, below I will describe some of them that are used today.

    Pressurized Water Reactors (PWR) these types of reactors use a pressurized vessel to contain the nuclear fuel, control rods, moderator, and coolant. The coolant and moderator  used is high pressurized water. The hot radioactive water that leaves the pressure vessel is looped through a steam generator, which in turn heats a secondary (non-radioactive) loop of water to steam that can run turbines. The majority of nuclear reactor are of this type, and are considered the safest and most reliable technology in current deployment. 

    Boiling Water Reactors (BWR) this type of reactor is similar to the PWR but without the steam generator. A boiling water reactor is cooled and moderated by water like a PWR, but at a lower pressure, which allows the water to boil inside the pressure vessel producing the steam that runs the turbines. In this case there is no primary and secondary loop. These reactors can have a higher thermal efficiency and can be more safe and stable than the PWR. 

    Pressurized Heavy Water Reactor (PHWR) these reactors ar of Canadian design (also know as CANDU) and are cooled by heavy water and moderated by pressurized water. The nuclear fuel is contained in hundreds of pressure tubes unlike the PWR where the fuel is contained in one large pressure vessel. The fossil fuel used is natural uranium (no need for enriched uranium) and the nuclear reactions are thermal-neutron acceptable. CANDUs have been built in Canada, Argentina, India, Pakistan, China, Romania and South Korea. 

    Reaktor Bolshoy Moschnosti Kanalniy (High Power Channel Reactor) (RBMK) this type of reactor is build to produce plutonium as well as power. They are water cooled and use graphite as a moderator. These reactors are in some way similar to the CANU by the fact that both can be refueled during power operation and use a pressure tube design rather than a pressurized vessel. However, unlike CANDU they are very unstable and large, making containment buildings for them expensive. Despite modern safety improvements, these types of reactors are considered the most dangerous reactors. The RBMKs have only been built in the former Soviet Union. 

    Gas Cooled Reactor (GCR) and Advanced Gas Cooled Reactor (AGCR) these reactors use graphite as a moderator and are cooled with carbon dioxide gas (CO2). They can have a high thermal efficiency compared with PWRs due to higher operating temperatures. There are a number of operating reactors of this design, mostly in the United Kingdom, where the concept was developed. 

    Liquid Metal Fast Breeder Reactor (LMFBR) this type of reactor is liquid metal cooled and the great thing about it is that it produces more fuel than it consumes. It is said that they "breed" fuel, mainly because of neutron capture. Their function is somehow similar to the PWR, but these reactors do not require high pressure containment because the liquid metal does not need to be kept at high pressure even at high temperatures. These reactors are fast neutron, not thermal neutron designs. There are 2 types of LMFBR:

          - Lead cooled: using liquid lead is a very good choice because of the great radiation shielding and operations can take place at very high temperatures. Also, lead is mostly transparent to neutrons, so fewer neutrons are lost in the coolant, and the coolant does not become radioactive. Lead is mostly inert, so there is less risk of explosions or accidents but such large quantities of lead can present a bit of a health hazard and can be problematic when disposal operations are due. 

          - Sodium cooled: Most LMFBRs are of this type. The sodium is relatively easy to obtain and work with, and it also manages to actually prevent corrosion on the various reactor parts immersed in it. However, sodium explodes violently when exposed to water, so care must be taken. 

    Pebble Bed Reactors (PBR) These use fuel molded into ceramic balls, and then circulate gas through the balls. The result is an efficient, low-maintenance, very safe reactor with inexpensive, standardized fuel. 

    Molten Salt Reactors. These dissolve the fuels in fluoride salts, or use fluoride salts for coolant. These have many safety features, high efficiency and a high power density suitable for vehicles. Notably, they have no high pressures or flammable components in the core.