Researchers from all over the world have been researching the aerodynamics of centrifugal compressors. They have explained many properties of the aerodynamic phenomena occurring in centrifugal compressors during their operation and have introduced various terms. This work presents the crucial knowledge that has been published on the flow instabilities occurring in centrifugal compressors operating at low flow rates. It also introduces the capabilities of the computational tools used for the simulation of these phenomena. The characteristic of the centrifugal compressor including highlighted areas of possible occurrence of typical flow instabilities is presented. This review is extended to include a frequency description of the vibroacoustic behavior related to these aerodynamic instabilities. The frequency description enables better identification of the given aerodynamic phenomena based on measurements or computations, and relevant sources of literature are provided. The researchers will receive a structured summary of key publications leading to the better understanding of the flow instabilities in centrifugal compressors.