Chemical propulsion uses the chemical reaction between a fuel and an oxidizer to generate heat that drives the expansion of a propellant in a rocket nozzle. The propellant is the product of the chemical reaction, for example water in the case of hydrogen and oxygen rocket engine.
A rocket engine is usually composed on an injection system, a reaction chamber and a nozzle. Most chemical rocket engines use pumps to feed the fuel and oxidizer into the reaction chamber, but pressure fed engines also are common, in particular for smaller thrusters.
Solid chemical engines are also possible. They are often used as booster stages for launch systems, such as for the US Space Shuttle.
Fuel page, for fuels that could be produced on Mars.