Microsystems with capabilities of acoustic signal perception and recognition are widely used in unattended monitoring applications. In order to realize long-term and large-scale monitoring, microsystems with ultra-low power consumption are always required. Acoustic wake-up is one of the solutions to effectively reduce the power consumption of microsystems, especially for monitoring sparse events. This paper presents a review of acoustic wake-up technologies for microsystems. Acoustic sensing, acoustic recognition, and system working mode switching are the basis for constructing acoustic wake-up microsystems. First, state-of-the-art MEMS acoustic transducers suitable for acoustic wake-up microsystems are investigated, including MEMS microphones, MEMS hydrophones, and MEMS acoustic switches. Acoustic transducers with low power consumption, high sensitivity, low noise, and small size are attributes needed by the acoustic wake-up microsystem. Next, acoustic features and acoustic classification algorithms for target and event recognition are studied and summarized. More acoustic features and more computation are generally required to achieve better recognition performance while consuming more power. After that, four different system wake-up architectures are summarized. Acoustic wake-up microsystems with absolutely zero power consumption in sleep mode can be realized in the architecture of zero-power recognition and zero-power sleep. Applications of acoustic wake-up microsystems are then elaborated, which are closely related to scientific research and our daily life. Finally, challenges and future research directions of acoustic wake-up microsystems are elaborated. With breakthroughs in software and hardware technologies, acoustic wake-up microsystems can be deployed for ultra-long-term and ultra-large-scale use in various fields, and play important roles in the Internet of Things.