This paper gives a review of acoustic and ultrasonic optical fiber sensors (OFSs). The review covers optical fiber sensing methods for detecting dynamic strain signals, including general sound and acoustic signals, high-frequency signals, i.e., ultrasonic/ultrasound, and other signals such as acoustic emissions, and impact induced dynamic strain. Several optical fiber sensing methods are included, in an attempted to summarize the majority of optical fiber sensing methods used to date. The OFS include single fiber sensors and optical fiber devices, fiber-optic interferometers, and fiber Bragg gratings (FBGs). The single fiber and fiber device sensors include optical fiber couplers, microbend sensors, refraction-based sensors, and other extrinsic intensity sensors. The optical fiber interferometers include Michelson, Mach-Zehnder, Fabry-Perot, Sagnac interferometers, as well as polarization and model interference. The specific applications addressed in this review include optical fiber hydrophones, biomedical sensors, and sensors for nondestructive evaluation and structural health monitoring. Future directions are outlined and proposed for acousto-ultrasonic OFS.