Abstract: A pump-jet propulsor is a multi-component integrated hydrodynamic propulsion device consisting of a guide tube, a rotating cascade (referred to as rotor) in the guide tube, and a stationary cascade (referred to as stator) in the guide tube. Pump-jet propulsor has the features of high critical sailing speed, heavy load, high propulsion efficiency, and low radiated noise. Pump-jet propulsor was first invented abroad in the middle of the last century, and mainly used for torpedo propulsion in the initial stage, and then extended to submarine propulsion. Nowadays, pump-jet propulsor is widely equipped in foreign submarines and high-speed torpedoes. There are great differences in pump-jet propulsor research and practical application at home and abroad. In recent years, pump-jet propulsor propulsion technology has become a research hotspot in the field of underwater equipment due to the technical blockade from abroad, the development needs of submarine equipment, and the extension of pump-jet propulsor application. The components of the pump-jet propulsor have complex flow interactions with each other, and the pump-jet propulsor is highly coupled with the hull. The application and popularization of pump-jet propulsors need a thorough understanding of hydrodynamic and flow field characteristics. This paper introduces the basic composition and characteristics of pump-jet propulsor and summarizes the research advance according to research interest and purpose. From the perspective of hydrodynamic characteristics, the propulsion features, prediction approaches, and hydrodynamic variation laws are summarized. From the perspective of flow field characteristics, the published investigations are categorized and summarized as tip clearance flow field, rotor-stator interference flow field, and wake flow field. This paper analyzes and summarizes the challenges in the research on hydrodynamic and flow field characteristics of pump-jet propulsor and the practical application of pump-jet propulsor. Finally, the prospect of further investigations on pump-jet propulsor is proposed.