Rehabilitation and nursing-care robots have become one of the prevalent methods for assistant treatment of motor disorder patients in the field of medical rehabilitation. Traditional rehabilitation robots are mostly made of rigid materials, which significantly limits their application for medical rehabilitation and nursing-care. Soft robots show great potential in the field of rehabilitation robots because of their inherent compliance and safety when they interact with humans. In this paper, we conduct a systematic summary and discussion on the soft rehabilitation and nursing-care robots. This study reviews typical mechanical structures, modeling methods, and control strategies of soft rehabilitation and nursing-care robots in recent years. We classify soft rehabilitation and nursing-care robots into two categories according to their actuation technology, one is based on tendon-driven actuation and the other is based on soft intelligent material actuation. Finally, we analyze and discuss the future directions and work about soft rehabilitation and nursing-care robots, which can provide useful guidance and help on the development of advanced soft rehabilitation and nursing-care robots.