Natural Language (NL) for transferring knowledge from a human to a robot. Recently, research on using NL to support human-robot cooperation (HRC) has received increasing attention in several domains such as robotic daily assistance, robotic health caregiving, intelligent manufacturing, autonomous navigation and robot social accompany. However, a high-level review that can reveal the realization process and the latest methodologies of using NL to facilitate HRC is missing. In this review, a comprehensive summary about the methodology development of natural-language-facilitated human-robot cooperation (NLC) has been made. We first analyzed driving forces for NLC developments. Then, with a temporal realization order, we reviewed three main steps of NLC: human NL understanding, knowledge representation, and knowledge-world mapping. Last, based on our paper review and perspectives, potential research trends in NLC was discussed. ; Comment: 30 pages, 15 figures, article submitted to Knowledge-based Systems, 2017 Jan