This paper reviews methods and applications of fault diagnosis and state detection in centrifugal pumps. Different studies show the most common faults and their effects: Failures of mechanical seals, roller bearings, and drives as well as leakage are prevalent. Since these might lead to a stand-still of pumps, automatic fault diagnosis can improve productivity. Fault definitions, methods of fault diagnosis and state detection functionalities in centrifugal pumps as well as their categorization regarding utilized models are presented. Reviewing applications of such in centrifugal pumps shows solutions from model-free fault detection to modelbased fault diagnosis. In those, impeller faults, cavitation and blockade/sedimentation receive the highest attention, while computation and sensor effort increases with method/model complexity. Two major research issues are the diagnosis of multiple fault cases and methods integrating a continuous monitoring and identification if a fault occurs.