Existing robots capable of climbing walls mostly rely on rigid actuators such as electric motors, but soft wall-climbing robots based on muscle-like actuators have not yet been achieved. Here, we report a tethered soft robot capable of climbing walls made of wood, paper, and glass at 90°with a speed of up to 0.75 body length per second and multimodal locomotion, including climbing, crawling, and turning. This soft wallclimbing robot is enabled by (i) dielectric-elastomer artificial muscles that generate fast periodic deformation of the soft robotic body, (ii) electroadhesive feet that give spatiotemporally controlled adhesion of different parts of the robot on the wall, and (iii) a control strategy that synchronizes the body deformation and feet electroadhesion for stable climbing. We further demonstrate that our soft robot could carry a camera to take videos in a vertical tunnel, change its body height to navigate through a confined space, and follow a labyrinth-like planar trajectory. Our soft robot mimicked the vertical climbing capability and the agile adaptive motions exhibited by soft organisms.