Additive manufacturing (AM) can be seen as a disruptive process that builds complex components layer upon layer. Two of its distinct technologies are Selective Laser Melting (SLM) and Electron Beam Melting (EBM), which are powder bed fusion processes that create metallic parts with the aid of a beam source. One of the most studied and manufactured superalloys in metal AM is the Ti–6Al–4V, which can be applied in the aerospace field due to its low density and high melting point, and in the biomedical area owing to its high corrosion resistance and excellent biocompatibility when in contact with tissues or bones of the human body. The research novelty of this work is the aggregation of all kinds of data from the last 20 years of investigation about Ti–6Al–4V parts manufactured via SLM and EBM, namely information related to residual stresses (RS), as well as the influence played by different heat treatments in reducing porosity and increasing mechanical properties. Throughout the report, it can be seen that the expected microstructure of the Ti–6Al–4V alloy is different in both manufacturing processes, mainly due to the distinct cooling rates. However, heat treatments can modify the microstructure, reduce RS, and increase the ductility, fatigue life, and hardness of the components. Furthermore, distinct post-treatments can induce compressive RS on the part’s surface, consequently enhancing the fatigue life.