Metal additive manufacturing (AM) is used to build and repair metal parts with heat input from a high-power beam (laser or electron beam) or electric arc (gas metal, gas tungsten, or gas plasma arc) and metal deposited layer by layer from powder or wire feedstock. This multiscale and multiphysics process is difficult to directly observe. It's modeling thus contributes to gaining process understanding. It can also support process parameter selection, process control, path planning, modeling and analysis of microstructure, distortion, and residual stress formed during metal AM. The sections of this chapter address first the electron beam, laser beam, and electric arc heat sources including their interaction with metal. Next, it covers process modeling with the thermal and thermo-fluid approaches and metal provided in the form of either powder or wire feedstock. Each of these sections includes a description of the physics taking place, the existing modeling approaches, the related assumptions and framework of application, open questions, as well as examples of knowledge the models provide access to.