Metal additive manufacturing (MAM) technology has great application potential in the aerospace, medical and energy fields with its high material utilization efficiency to achieve the manufacturing of metal parts of any shape. However, the extreme thermal, mechanical, and metallurgical coupling in MAM process leads to large residual stresses in the manufactured samples. Residual stress has a significant effect on the dimensional stability, corrosion resistance, crack growth resistance and mechanical properties of MAM samples. As a result, residual stress can be regarded as a key factor in controlling costs, enhancing product efficiency and quality. To help researchers and engineers attain up-to-date information and knowledge about residual stress in MAM, the current paper provides a comprehensive review in this field, especially the formation mechanisms, the influence of process parameters, prediction and control methods.