Additive manufacturing has made significant progress in recent years, and metal additive manufacturing can 3D fabricate complex-shaped parts with high precision, which has unique advantages in applications of various industries.However, the high temperature gradient in the forming of metal additive manufacturing parts can cause complex residual stresses. In this review, the characteristics of additive manufacturing technology are briefly analyzed, and the processing principles of selective laser melting and wire and arc additive manufacturing technology are emphatically summarized. On this basis, the generation mechanism and measurement method of residual stress from the additive manufacturing process are reviewed in detail. The temperature gradient mechanism is the most commonly used method to explain the residual stress generation. Regarding the measurement of residual stress, it is summarized from two aspects of non-destructive testing and destructive testing. The common destructive testing methods for residual stress are profile method and drilling method, while the common non-destructive testing method is X-ray diffraction method. The control methods of residual stress are also summarized, including processing parameters optimization,preheating and slow cooling and remelting, structural design,auxiliary external field, post-processing. Finally, a brief summary of the residual stress research in additive manufacturing of metal structural parts and the problems to be solved are summarized, and the development direction of additive manufacturing is prospected.