Natural-language-facilitated human-robot cooperation (NLC), in which natural language (NL) is used to share knowledge between a human and a robot for conducting intuitive human-robot cooperation (HRC), is continuously developing in the recent decade. Currently, NLC is used in several robotic domains such as manufacturing, daily assistance and health caregiving. It is necessary to summarize current NLC-based robotic systems and discuss the future developing trends, providing helpful information for future NLC research. In this review, we first analyzed the driving forces behind the NLC research. Regarding to a robot s cognition level during the cooperation, the NLC implementations then were categorized into four types {NL-based control, NL-based robot training, NL-based task execution, NL-based social companion} for comparison and discussion. Last based on our perspective and comprehensive paper review, the future research trends were discussed. ; Comment: 21 pages, 10 figures, article submitted to Knowledge-based Systems, 2017 Jan