The last decade has witnessed an increasing interest in the more active use of soft materials in robotic systems. Having a soft body like the ones in biological systems can potentially provide a robot with superior capabilities. For example, soft body can help the robots to adaptively navigate through small openings, softness can prevent injuries in human-robot interaction, while deformable body can also store and release energy, which may lead to energy effciency in locomotion tasks. By building robotic systems with soft materials, we can realize systems that are safer, cheaper, and more adaptable than the level that conventional rigid-material robots can achieve. Soft-Material Robotics introduces the fundamental aspects of this vibrant research topic from history, modelling, control, and system integration. This content sets it apart from previous review efforts that have focused on presenting individual case studies.