The gas-generator cycle is a power cycle of a bipropellant rocket engine. Some of the propellant is burned in a gas generator and the resulting hot gas is used to power the engine's pumps. The gas is then exhausted. Because something is "thrown away" this type of engine is also known as open cycle.
There are several advantages to the gas-generator cycle over its counterpart, the staged combustion cycle. The gas generator turbine does not need to deal with the counter pressure of injecting the exhaust into the combustion chamber. This simplifies plumbing and turbine design, and results in a less expensive and lighter engine.
The main disadvantage is lost efficiency due to discarded propellant. Gas-generator cycles tend to have lower specific impulse than staged combustion cycles. However, there are forms of the gas-generator cycle that recycle the exhaust into the nozzle of the rocket engine. This is seen in the F-1 and Merlin 1D Vacuum rocket engines used on the Saturn V booster stage and the Falcon 9 second stage, respectively.
As in most cryogenic rocket engines, some of the fuel in a gas-generator cycle may be used to cool the nozzle and combustion chamber (regenerative cooling).  The ultimate performance of a rocket engine is primarily limited by the ability of the construction materials to withstand the extreme temperatures of rocket combustion processes, as a higher temperature directly increases the local speed of sound that limits exhaust velocity. 
Some engines, including the RD-107 used on the Soyuz, use a third fuel, typically Hydrogen peroxide, which decomposes as it passes over a catalyst producing gasses which are used to drive the turbines. Engines using this system are mechanically simple, but have poor specific impulse.
Gas-generator combustion engines include the following:
Rocket launch systems that use gas-generator combustion engines: