In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.