Corrosion failure, especially stress corrosion cracking and corrosion fatigue, is the main cause of centrifugal compressor impeller failure. And it is concealed and destructive. This paper summarizes the main theories of stress corrosion cracking and corrosion fatigue and its latest developments, and it also points out that existing stress corrosion cracking theories can be reduced to the anodic dissolution (AD), the hydrogen-induced cracking (HIC), and the combined AD and HIC mechanisms. The corrosion behavior and the mechanism of corrosion fatigue in the crack propagation stage are similar to stress corrosion cracking. The effects of stress ratio, loading frequency, and corrosive medium on the corrosion fatigue crack propagation rate are analyzed and summarized. The corrosion behavior and the mechanism of stress corrosion cracking and corrosion fatigue in corrosive environments, which contain sulfide, chlorides, and carbonate, are analyzed. The working environments of the centrifugal compressor impeller show the behavior and the mechanism of stress corrosion cracking and corrosion fatigue in different corrosive environments. The current research methods for centrifugal compressor impeller corrosion failure are analyzed. Physical analysis, numerical simulation, and the fluid-structure interaction method play an increasingly important role in the research on impeller deformation and stress distribution caused by the joint action of aerodynamic load and centrifugal load.