With years of development and accumulation, a considerable amount of research has focused on micro-motion, an important auxiliary feature in radar target detection and recognition. With the recent rise of terahertz, micro-motion feature extraction in the terahertz region has increasingly highlighted its advantages. Herein, we systematically surveyed the recent research on terahertz radar micro-motion feature extraction and discussed micro-motion feature analysis, micro-motion feature extraction, and micro-motion target imaging. And then we emphatically introduced the work of our research team, including the theoretical and experimental research on micro-motion feature analysis, micro-motion feature extraction and high-resolution/high-frame micro-motion target imaging. Furthermore, we analyzed the growing trend of micro-motion feature extraction in the terahertz region, and pointed out the new technology directions worth to be studied further and the technical challenges to be solved.