Acoustic signals are important markers to monitor physiological and pathological conditions, e.g., heart and respiratory sounds. The employment of traditional devices, such as stethoscopes, has been progressively superseded by new miniaturized devices, usually identified as microelectromechanical systems (MEMS). These tools are able to better detect the vibrational content of acoustic signals in order to provide a more reliable description of their features (e.g., amplitude, frequency bandwidth). Starting from the description of the structure and working principles of MEMS, we provide a review of their emerging applications in the healthcare field, discussing the advantages and limitations of each framework. Finally, we deliver a discussion on the lessons learned from the literature, and the open questions and challenges in the field that the scientific community must address in the near future.