Additive manufacturing (AM) has been established as powerful tool to produce parts with complex shapes, sometimes impossible to manufacture by conventional processes. The high thermal gradients and high cooling rates applied during AM promotes a refined microstructure with anisotropic behaviour, which will influence the mechanical behavior of the built parts. Different aluminum alloys can be processed by AM, and the microstructural and mechanical properties of the parts are closely linked to the parameters used during the process. However, the intrinsic characteristics of the process and raw material can generate defects such as the formation of pores, cracks, and considerable surface roughness. Likewise, the characteristics of the process may prevent the formation of reinforcement phases that allow the mechanical strength to be increased. Therefore, various investigations have been dedicated to studying the effect of applying heat treatments on aluminum parts produced by AM and their effects on microstructure, defect reduction, mechanical behavior, and their correlation with heat treatment parameters used in conventionally produced aluminum parts. Considering the above, the present review describes the heat treatments currently applied to cast, wrought, and miscellaneous aluminum alloys processed by AM on their microstructural and mechanical characteristics. Finally, future trends and perspectives related to the application of heat treatments in aluminum parts built by AM will be proposed.