This paper reviews the current status of soft robots in biomedical field. Soft robots are made of materials that have comparable modulus of elasticity to that of biological systems. Several advantages of soft robots over rigid robots are safe human interaction, ease of adaptation with wearable electronics and simpler gripping. We review design factors of soft robots including modeling, controls, actuation, fabrication and application, as well as their limitations and future work. For modeling, we survey kinematic, multibody and numerical finite element methods. Finite element methods are better suited for the analysis of soft robots, since they can accurately model nonlinearities in geometry and materials. However, their real-time integration with controls is challenging. We categorize the controls of soft robots as model-based and model-free. Model-free controllers do not rely on an explicit analytical or numerical model of the soft robot to perform actuation. Actuation is the ability to exert a force using actuators such as shape memory alloys, fluid gels, elastomers and piezoelectrics. Nonlinear geometry and materials of soft robots restrict using conventional rigid body controls. The fabrication techniques used for soft robots differ significantly from that of rigid robots. We survey a wide range of techniques used for fabrication of soft robots from simple molding to more advanced additive manufacturing methods such as 3D printing. We discuss the applications and limitations of biomedical soft robots covering aspects such as functionality, ease of use and cost. The paper concludes with the future discoveries in the emerging field of soft robots.