Flexible and wearable acoustic wave technology has recently attracted tremendous attention due to their wide-range applications in wearable electronics, sensing, acoustofluidics, and lab-on-a-chip, attributed to its advantages such as low power consumption, small size, easy fabrication, and passive/wireless capabilities. Great effort has recently been made in technology development, fabrication, and characterization of rationally designed structures for next-generation acoustic wave based flexible electronics. Herein, advances in fundamental principles, design, fabrication, and applications of flexible and wearable acoustic wave devices are reviewed. Challenges in material selections (including both flexible substrate and piezoelectric film) and structural designs for high-performance flexible and wearable acoustic wave devices are discussed. Recent advances in fabrication strategies, wave mode theory, working mechanisms, bending behavior, and performance/evaluation are reviewed. Key applications in wearable and flexible sensors and acoustofluidics, as well as lab-on-a-chip systems, are discussed. Finally, major challenges and future perspectives in this field are highlighted.