The locomotion of soft robotics is becoming an emerging research frontier since it is extremely crucial for designing and fabricating soft machines that can implement usual robotic functions. Despite some recent success of soft robots locomoting on horizontal and lightly-tilt surfaces, it is still a great challenge to achieve climbing of soft robots on wall or vertical surfaces due to the lack of effective switchable adhesion actuators to counter the gravity. The climbing soft robots could largely expand the horizons of soft robotics in their potential applications in intelligent surveillance, inspection, and detection. In addition, it could become more challenging if the soft machine is required to carry a certain load when climbing on multiple types of surfaces. In this talk, we propose a new octopus-inspired adhesion actuator that allows for rapid, strong and switchable adhesion upon pneumatic actuation. Rather than the conventional way of applying negative pressure to the suction actuator, we use positive pressure to actuate the switchable adhesion. The adhesion actuator demonstrates strong adhesion forces, which exhibits a strong loading capacity of 60-80 times the weight of adhesion actuator itself on vertical surfaces, as well as on a variety of surfaces: wet (slippery), dry, smooth and semi-smooth. Based on this adhesion actuator, we build a novel and simple inchworm-inspired soft robot which can walk and climb vertically on smooth and semi-smooth surfaces with great loading capability of five times its own weight. Furthermore, this soft robot can also walk and climb under water as smoothly as on the ground. We demonstrate that the bio-inspired soft robots can achieve climbing on different types of vertical smooth and semi-smooth surfaces, including dry, wet, slippery, and underwater surfaces.