In conventional robotics, the technological research focuses on strength and functionality of robots. Recently, out of these perspective, soft robot, which is new shape of robots inspired from biological systems attracts intensive interest in fields of robotics. Inspired from nature, we could improve the mechanical properties of conventional robots and impart new kinds of biological functions to robots. Many innovative strategies have been developed in recent years to design soft components and systems that realizes natural actuations of bioinspired robot. Soft robots consist of soft materials and are actuated by various kinds of mechanical principles. There are several advantages of soft robots compared to the conventional robots; safe human-machine interactions, adaptive conformability to wearable devices, useful biological properties from organism etc. Due to the unique features and advantages, soft robots have a considerable range of applications. The purpose of this study is investigation of state of art technologies regarding mechanical and material aspects of soft robots. This review was written in three fundamental sections: i) Materials for soft robotics, ii) fundamental mechanics of soft materials and, iii) mechanical principles of actuation. The promising soft materials can be categorized simply in four types according to softness and functions: hydrogel, elastomer, shape memory polymer and self-healing polymer. These materials have softness and deformation freedom, which has potential to provide natural movements of robot enabling imitation of biological movements. To analyze it in scientific method, we investigate the several mechanical standards and principles of robot actuation in mechanical aspects. In the future, all robots would evolve closer to biological lives.