Combustion instability is a major problem to be solved in the gas turbine community. The unsteady flow dynamics in the combustor is caused by the interaction of the flame and flow characteristics in the system. The oscillations are studied using acoustic analysis and wave equations. In order to understand the source for the unsteadiness in the flow, the effect of heat release in the system on the acoustic variations present in the combustor should also be studied. Instabilities are triggered by the interactions, which resonate between the process and the modes within a system which leads to the creation of disturbances in the flow resulting in unwarranted characteristics in the system. Some of the effects include increase in vibrations of structure, high heat transfers at the wall, occurrence of flashback and blow off of the flame. Over the years, research has been carried out by different groups in understanding the primary mechanisms of onset of combustion instabilities and various types of control systems to dampen the amplitude of the oscillations. In this article, we reviewed the analytical, experimental and numerical work studying the major instability mechanisms in gas turbine combustors.