Drawing inspiration from the jumping motions of living creatures in nature, jumping robots have emerged as a promising research field over the past few decades due to great application potential in interstellar exploration, military reconnaissance, and life rescue missions. Early reviews mainly focused on jumping robots made of lightweight and rigid materials with mechanical components, concentrating on jumping control and stability. Herein, attention is paid to the jumping mechanisms of soft actuators assembled from various soft smarting materials and powered by different stimulus sources. The challenges and prospects of soft jumping actuators are also discussed. It is hoped that this review will contribute to the further development of soft jumping actuators and broaden their practical applications.