Additive manufacturing (AM) possesses tremendous potential in controlling epitaxial growth of deposited materials, and thus attempts have been made to employ AM technology to fabricate or repair single‐crystal (SX) metal parts in recent years. One of the key issues in producing SX structures is the elimination of stray grain (SG) formation, but the layer‐wise fabrication nature of AM processes makes SGs difficult to avoid. Herein, the state‐of‐the‐art developments in this emerging research area are surveyed. It introduces the fundamental mechanisms of epitaxial growth in AM, summarizes the recent innovations and findings on using AM techniques to assist epitaxial growth and avoid SGs for SX metallic materials, discusses the relation of stray‐grain avoidance and crack‐free microstructure, and reviews the analytical and numerical modeling efforts for epitaxial growth and texture control. In addition, the challenges in achieving defect‐free SX microstructure are discussed, such that future research directions are pointed out. It is believed that this critical review provides insights on microstructure control for AM‐produced metallic materials and lays a solid foundation to stimulate more rigorous research.