Acoustic sensing and monitoring are important techniques for structural health monitoring, marine exploration, biomedicine, etc. In contrast to conventional electrical acoustic sensors, fiber-optic acoustic sensors (FOASs) offer distinct advantages, including immunity to electromagnetic interference, enhanced sensitivity, and expanded bandwidth. In this review, FOASs have been divided into acoustic-structure-optic coupling (ASOC) type and acoustic-optic coupling (AOC) type according to the activation of the acoustic signal on the optical signal. The sensing principles of FOASs have been introduced, mainly including intensity-based, fiber Bragg grating(FBG)-based, and Fabry-P & eacute;rot (F-P) interferometer(FPI)-based. Besides, the research progress of ASOC-FOASs and AOC-FOASs has been presented and discussed in detail. The current status of the application of FOASs in nondestructive testing, underwater acoustic monitoring, bioimaging, and partial discharge monitoring has been summarized. The limitations and future tendencies of FOASs have been discussed as well.