We present an overview of recent developments in the area of acoustic sensing that is inspired by biology and realized by micro-electromechanical systems (MEMS). To support understanding, an overview of the principles of human hearing is presented first. After the review of bio-inspired sensing systems, we continue with an outline of an adaptable acoustic MEMS-based sensor that offers adaptable sensing properties due to a simple, real-time feedback. The transducer itself is based on an active cantilever, which offers the advantage of an integrated deflection sensing based on piezoresistive elements and an integrated actuation using thermomechanical effects. We use a feedback loop, which is realized via a field-programmable gate array or analog circuits, to tune the dynamics of the sensor system. Thereby, the transfer characteristics can be switched between active, linear mode, for which the sensitivity and minimal detectable sound pressure level can be set by the feedback strength (similar to control of the quality factor), and an active nonlinear mode with compressive characteristics. The presented sensing system, which is discussed both from an experimental and theoretical point of view, offers real-time control for adaptation to different environments and application-specific sound detection with either linear or nonlinear characteristics.