The emerging field of soft robotics makes use of many classes of materials including metals, low glass transition temperature (Tg) plastics, and high Tg elastomers. Dependent on the specific design, all of these materials may result in extrinsically soft robots. Organic elastomers, however, have elastic moduli ranging from tens of megapascals down to kilopascals; robots composed of such materials are intrinsically soft − they are always compliant independent of their shape. This class of soft machines has been used to reduce control complexity and manufacturing cost of robots, while enabling sophisticated and novel functionalities often in direct contact with humans. This review focuses on a particular type of intrinsically soft, elastomeric robot − those powered via fluidic pressurization. This manuscript presents a comprehensive review of the materials, design, and manufacturing of fluidically pressurized intrinsically soft robotics, and set a historical context for their development. The authors then discuss their applications for human interaction and speculate on future composition and use cases.