Natural-language-facilitated human-robot cooperation (NLC) refers to using natural language (NL) to facilitate interactive information sharing and task executions with a common goal constraint between robots and humans. Recently, NLC research has received increasing attention. Typical NLC scenarios include robotic daily assistance, robotic health caregiving, intelligent manufacturing, autonomous navigation, and robot social accompany. However, a thorough review, that can reveal latest methodologies to use NL to facilitate human-robot cooperation, is missing. In this review, a comprehensive summary about methodologies for NLC is presented. NLC research includes three main research focuses: NL instruction understanding, NLbased execution plan generation, and knowledgeworld mapping. In-depth analyses on theoretical methods, applications, and model advantages and disadvantages are made. Based on our paper review and perspective, potential research directions of NLC are summarized. Index Terms-natural language, human-robot cooperation, NL instruction understanding, NLbased execution plan generation, knowledge-world mapping _______________________________________ Rui Liu and Xiaoli Zhang are with the Intelligent Robotics and Systems Lab (IRSL), Colorado School of Mines,