In recent years, Light Detection and Ranging (LiDAR) has been drawing extensive attention both in academia and industry because of the increasing demand for autonomous vehicles. LiDAR is believed to be the crucial sensor for autonomous driving and flying, as it can provide high-density point clouds with accurate three-dimensional information. This review presents an extensive overview of Microelectronechanical Systems (MEMS) scanning mirrors specifically for applications in LiDAR systems. MEMS mirror-based laser scanners have unrivalled advantages in terms of size, speed and cost over other types of laser scanners, making them ideal for LiDAR in a wide range of applications. A figure of merit (FoM) is defined for MEMS mirrors in LiDAR scanners in terms of aperture size, field of view (FoV) and resonant frequency. Various MEMS mirrors based on different actuation mechanisms are compared using the FoM. Finally, a preliminary assessment of off-the-shelf MEMS scanned LiDAR systems is given.