Origami, the ancient paper folding art has inspired the engineering equipment and design for decades. The basic concept of origami is very general, which leads to applications ranging from small scale to large scale. Recently, researchers are interested in being able to create self-folding structures. Such a structure enables kinematic manipulation by external forces or moments without folding and/or unfolding operations. This is a beneficial application for many fields including aerospace systems, robots, small devices and self-assembly systems. In this paper, the investigation and analyses of the previous literatures on the key driving force of the actuation structure, including the heat, light, electricity, gas and other actuation methods. The aims are to provide researchers and practitioners with the support to systematically understand the latest technologies in this important and evolving field, with inspiration and direction for follow-up.