Soft-bodied manipulators are new type of mechanical devices mainly made of soft materials,which possess the characteristics of high flexibility,good adaptation in complex environment and safe human-machine interaction because of the flexibility and passive adaptability of soft materials. The soft-bodied manipulators have been intensively studied and shown great potential applications. The review of existing soft-bodied manipulators in terms of applications,actuation methods,materials and fabrication,modeling and control is presented. The current issues and possible solutions are also discussed. Soft-bodied manipulators are an important branch of soft robotics,which involves a combination of material science,mechanics,chemistry,mechanical design and manufacture,electronic and control science and biology. The study of soft-bodied manipulators will greatly enrich people’s understanding of the complex and rich characteristics of soft materials,and will provide theoretical and technical guidance for integrating soft materials into design of products.