The distortion and residual stress in the metal additive manufacturing have a certain influence on the forming process and the performance of the parts. There are many factors that can influence the distortion and residual stress. The evolutions of the distortion and residual stress in the additive manufacturing process have not been clearly revealed. We review the research status of distortion and residual stress in metal additive manufacturing, and then summarize some laws about them. In addition, we propose the concept of “constraining force”, which can help others more distinctly understand the mechanism of distortion and residual stress in metal additive manufacturing.