Demographic change in the world is a reality, and as a result, the number of elderly people is growing in both developed and developing countries, posing several social and economic issues. Most elderly people choose to stay alone at home rather than living with their families who can take care of them. Robots have the potential to revolutionize elderly care by providing aid, companionship, and monitoring services. The objective of this study is to present a comprehensive review which summarizes the cutting-edge works in adapting robotic applications to improve the quality of life for the elderly. We compare paradigms thoroughly and methodically in terms of support, guidance, health monitoring, and usability. We then summarize the current achievements while acknowledging their limitations before presenting perspectives on highly promising future work.