Gas bubbles present in liquids underpin many natural phenomena and human-developed technologies that improve the quality of life. Since all living organisms are predominantly made of water, they may also contain bubbles—introduced both naturally and artificially—that can serve as biomechanical sensors operating in hard-to-reach places inside a living body and emitting signals that can be detected by common equipment used in ultrasound and photoacoustic imaging procedures. This kind of biosensor is the focus of the present article, where we critically review the emergent sensing technologies based on acoustically driven oscillations of bubbles in liquids and bodily fluids. This review is intended for a broad biosensing community and transdisciplinary researchers translating novel ideas from theory to experiment and then to practice. To this end, all discussions in this review are written in a language that is accessible to non-experts in specific fields of acoustics, fluid dynamics and acousto-optics.