Using metal additive manufacturing processes can make up for traditional forging technologies when forming complex-shaped parts. At the same time, metal additive manufacturing has a fast forming speed and excellent manufacturing flexibility, so it is widely used in the aerospace industry and other fields. The fatigue strength of metal additive manufacturing is related to the microstructure of the epitaxially grown columnar grains and crystallographic texture. The crystal plasticity finite element method is widely used in the numerical simulation of the microstructure and macro-mechanical response of materials, which provides a strengthening and toughening treatment and can reveal the inner rules of material deformation. This paper briefly introduces common metal additive manufacturing processes. In terms of additive manufacturing fatigue, crystal plasticity simulations are summarized and discussed with regard to several important influencing factors, such as the microstructure, defects, surface quality, and residual stress.