Pneumatic and inflatable structures
The most common approach to soft actuation is pneumatic, using air pressure to change a structure's shape. A typical pneumatic soft actuator is built from a flexible chamber, often molded silicone or a flexible polymer, with internal channels or ribbing designed so that inflating the chamber with air causes it to bend, curl, or extend in a predictable, engineered direction rather than just ballooning outward uniformly. Stacking or combining several of these chambers lets designers build fingers that curl around an object, tentacle-like arms that reach and wrap, or whole robot bodies that crawl by sequentially inflating and deflating different sections.
This approach is popular because it's mechanically simple, a soft pneumatic actuator has no motors, gears, or rigid linkages inside it, just an air supply and a flexible chamber shaped to deform in a useful way. That simplicity is also why octopus-inspired soft grippers are such a widely cited research direction, an octopus arm has no rigid skeleton at all, and soft pneumatic and muscle-like actuators are the closest engineering analog researchers have found to reproducing that kind of boneless, continuously deformable reach and grip.