Computer numerical control (CNC) machine tools are widely used in various industrial fields ranging from aerospace, automotive, ship building, and the die/mould to manufacture products. However, tool paths of most CNC machine tools are composed of a series of linear motion commands (G01), which will inevitably cause the discontinuity in curvature and feedrate at the junctions between adjacent linear tool path segments, deteriorating the surface quality with unfavorable marks and decreasing the machining efficiency. To solve this problem for obtaining the steady and continuous motions of machine tools, the local corners have to be smoothed. Generally, the existing corner smoothing methods can be classified as the global smoothing and the local corner smoothing, where the specially designed transition curves or the directly planned motion of machine tools are adopted to generate the geometrically corner-free tool path. Moreover, some new methods that focus on developing different transition or rounding strategies are also developed for further improving the kinematics performance of machine tools. In this paper, the recent advances and researches on corner smoothing methods are reviewed from different categories, and the conclusions, remaining challenges and future directions in corner smoothing are also presented.