Flexible and stretchable microdevices incorporate highly deformable structures, facilitating precise functionality at the micro- and millimetre scale. Flexible microdevices have showcased extensive utility in the fields of biomedicine, microfluidics, and soft robotics. Actuation plays a critical role in transforming energy between different forms, ensuring the effective operation of devices. However, when it comes to actuating flexible microdevices at the small millimetre or even microscale, translating actuation mechanisms from conventional rigid large-scale devices is not straightforward. The recent development of actuation mechanisms leverages the benefits of device flexibility, particularly in transforming conventional actuation concepts into more efficient approaches for flexible devices. Despite many reviews on soft robotics, flexible electronics, and flexible microfluidics, a specific and systematic review of the actuation mechanisms for flexible and stretchable microdevices is still lacking. Therefore, the present review aims to address this gap by providing a comprehensive overview of state-of-the-art actuation mechanisms for flexible and stretchable microdevices. We elaborate on the different actuation mechanisms based on fluid pressure, electric, magnetic, mechanical, and chemical sources, thoroughly examining and comparing the structure designs, characteristics, performance, advantages, and drawbacks of these diverse actuation mechanisms. Furthermore, the review explores the pivotal role of materials and fabrication techniques in the development of flexible and stretchable microdevices. Finally, we summarise the applications of these devices in biomedicine and soft robotics and provide perspectives on current and future research.