Additive manufactured magnesium (Mg) alloys have widespread applications in the medical industry as orthopedic implants and biomedical stents, and in the transportation/automotive industry due to their status as the lightest structural metallic alloys. The printability of Mg alloys is challenging due to the high oxidization rate, rapid evaporation, and susceptibility to gas trapping. Accordingly, there might be many defects in the as-built parts such as cracking and delamination, porosity and lack of fusion, residual/thermal stresses and distortion, inhomogeneous/columnar microstructure, anisotropy in mechanical/physical properties, inclusions, and non-equilibrium phases formed during solidification. The removal of these defects has a great practical significance, where the post-processing heat treatments without altering the geometry of the parts are often sought in this regard. Accordingly, the present overview article focuses on and critically discusses the recent progress/advances in the application of hot isostatic pressing (HIP), solution annealing (solutionizing), and aging/precipitation heat treatment for the modification/homogenization of the microstructure and improvement of mechanical/functional properties of Mg alloys for the first time. The main fabrication methods are selective laser melting (SLM) from the category of powder bed fusion (PBF) processes, as well as wire and arc additive manufacturing (WAAM) from the category of directed energy deposition (DED) processes. Moreover, the adaptation of the friction stir processing (FSP) technology into additive manufacturing for grain refinement via dynamic recrystallization (DRX) and defect/pore closure (due to the elevated-temperature thermomechanical processing effects), combined severe plastic deformation (SPD) and thermal post-processing, hybridization of additive manufacturing for Mg alloys, and future prospects have been summarized.