A metal additive manufacturing process results in a nearly net-shaped fabrication of parts directly from digital data. A local heat source melts the deposited material, and a part is built layer-by-layer. Residual stress and deformation are critical issues experienced by additively manufactured parts. Modeling the additive manufacturing process provides important insights and can help determine an optimal build plan so as to minimize residual stress formation. Various approaches have been used for modeling of residual stresses, ranging from high-fidelity models to simplified models, for quicker results. This paper provides a state-of-the-art review of the approaches used to numerically model residual deformation and stresses in structures built using additive manufacturing. Furthermore, it describes the physical causes of residual-stress generation in an additively manufactured structure.