Soft robots present the opportunity to extend the capabilities currently demonstrated within the field of robotics. By utilizing primarily soft materials in their construction, soft robots are inherently safe to operate around humans, can handle delicate tasks without advanced controls, and are robust to shocks and impacts during deployment. While proof-of-concept devices have been demonstrated successfully, there remains a need for widely applicable, reliable soft robotic components. This dissertation presents sensors to reliably measure the large deformations exhibited in soft robotic structures and responsive structures enabled by variable stiffness materials that can switch from flexible to stiff on-demand. By characterizing the sensors from the material level, through the manufacturing, to the completed functional device, the fabrication processes can be depended upon to produce sensors with predictable, reliable performance. The sensors were applied to various soft robotic systems through implementation on the surface of the structures to measure surface strains, and embedded in the body of the robot to measure body deformations. The sensory feedback was used to reconstruct the state of and to perform closed-loop control of the soft robot's position. Variable stiffness materials that switch from rigid to soft through application of heat were leveraged to create responsive structures that can be deformed or reconfigured on-demand. This capability is necessary for soft robots to exert load onto the external environment and enables a wider range of interactions with target objects. The work presented in this dissertation furthers the field of soft robotics by illustrating a path toward proven, reliable soft sensors for measuring large strains and variable stiffness materials to create responsive structures.