Faced with the increasingly severe global aging population with fewer children, the research, development, and application of elderly-care robots are expected to provide some technical means to solve the problems of elderly care, disability and semi-disability nursing, and rehabilitation. Elderly-care robots involve biomechanics, computer science, automatic control, ethics, and other fields of ... [Show full abstract] knowledge, which is one of the most challenging and most concerned research fields of robotics. Unlike other robots, elderly-care robots work for the frail elderly. There is information exchange and energy exchange between people and robots, and the safe human-robot interaction methods are the research core and key technology. The states of the art of elderly-care robots and their various nursing modes and safe interaction methods are introduced and discussed in this paper. To conclude, considering the disparity between current elderly care robots and their anticipated objectives, we offer a comprehensive overview of the critical technologies and research trends that impact and enhance the feasibility and acceptance of elderly care robots. These areas encompass the collaborative assistance of diverse assistive robots, the establishment of a novel smart home care model for elderly individuals using sensor networks, the optimization of robot design for improved flexibility, and the enhancement of robot acceptability.