The layer-by-layer construction process, as well as the high cooling rates and high thermal gradients offered in different additive manufacturing (AM) techniques, directly influence the microstructural characteristics and mechanical behavior of the built metallic parts. They are characterized by presenting a highly refined and anisotropic structure with columnar grains. Likewise, the intrinsic thermal treatments generated by the continuous heating-cooling of the different layers and the characteristics of the process can also generate changes and microstructural defects that affect the integrity of the parts and their mechanical behavior. Because of this, various heat treatments have been applied to improve the structural integrity and mechanical behaviour of AM parts. Due to the initial microstructural characteristics, the conditions and types of heat treatment applied to AM parts often differ from those applied to parts built using conventional processes. Considering the above, this review focuses on summarizing the heat treatments applied to metal parts produced by AM and their comparison with standardized processes. These differences will be discussed in microstructural characteristics, phase formation, defect reduction, and mechanical properties. Also, some key issues and prospects are highlighted and discussed.