The aging population is growing at an unprecedented rate globally and robotics-enabled solutions are being developed to provide better independent living for older adults. In this study, we report the results from a systematic review of the state-of-the-art in home robotics research for caring for older adults. This review aims to address two questions: (1) What research is being done towards integrating robotics for caring for older adults? (2) What are the research and technology challenges that robots are facing in the home? Sixty-three papers have been identified and studied in this review by following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Common themes that are consistent across the reviewed papers are distinguished and consolidated as follows: (1) Ambient assisted living, where smart home environments and physical support tools are studied; (2) Robot ecosystem, where robotic devices are used to provide various services; (3) Social interaction, where the social isolation problem has been targeted. We also summarize the results of similar literature reviews we came across during our search. The results of this study present the current research trends and technologies used in each category. The challenges and limitations of robotics applications are also identified. Suggestions for accelerating the deployment of robots at home for providing older adults with independent care in the home are presented based on the results and insights from this study.