Abstract: Propeller noise is widespread in the fields of aeronautics and underwater systems, and represents a significant and difficult problem in aeroacoustics. Propeller noise problem is closely related to spatially and temporally inhomogeneous and anisotropic turbulent flows as well as complex interactions between multi-scale turbulent structures and rotating blades, which request further investigations. To show potential research directions in the near future, this article first introduces the baseline problem of flow-induced noise of propellers, and elaborates the history of propeller noise studies in the past half-century. Next, the research progresses of propeller noise in theoretical, experimental, and computational studies are analyzed and summarized, with the emphasis on some unresolved difficult problems. Then, some fundamental and important aerodynamic problems of propeller noise, including the rotor-stator interaction noise and boundary-layer ingestion noise, are introduced. Last but not least, the related important applications such as next-generation aircrafts, unmanned aerial vehicles, and underwater systems are discussed. The corresponding future development directions and potential applications of the propeller noise problem are proposed at the end of this article.