The review of the liquid propellant rocket engine is presented. The combustion instabilities which were discovered on solid and liquid propellant rocket engines in 1930, have occurred on propulsion devices, such as gas turbine, ramjet, scramjet and rocket, and thus a study on the combustion instability became necessary. However, this problem has not been solved yet. Therefore, we investigated causes and mechanisms of the combustion instability and surveyed the efforts of solving combustion instability in various countries for developing stable liquid propellant rocket engines.