In order to master the atomization characteristics of oscillating spray and its relationship with unstable combustion, research and development of gas-liquid coaxial swirl injectors and liquid-liquid coaxial swirl injectors, which are widely used in liquid rocket engines, are reviewed from three aspects of excited oscillation, self-pulsation, and interactions of spray oscillation with combustion stability, so as to deepen our understanding of them. According to the review, for the excited oscillation, the research on the upstream pressure oscillation caused by flow oscillation of supply system under normal temperature and pressure conditions is relatively sufficient. However, the research on the backpressure oscillation caused by pressure oscillation in the combustion chamber and the research on the excited oscillation of spray under supercritical conditions are lack. For the self-pulsation, the current research is focused on the liquid-centered coaxial swirl injectors. There are few studies on the gas-centered coaxial swirl injectors and liquid-liquid coaxial swirl injectors. The optical diagnosis technology is far from enough to extract the single combustion flow field information.