In recent years, metal additive manufacturing developed intensively and became a relevant technology in industrial production of highly complex and function integrated parts. However, almost all additively manufactured parts must be post-processed in order to fulfil geometric tolerances, surface quality demands and the desired functional properties. Thus, additive manufacturing actually means the implementation of additive-subtractive process chains. Starting with the most relevant additive processes (powder-based PBF-LB, LMD-p and wire-based WAAM and LMD-w/WLAM), considering intermediate process steps (heat treatment and shot peening) and ending up with post-processing material removal processes (with defined and undefined cutting edges), this paper gives an overview of recent research findings with respect to a comprehensive scientific investigation of influences and interactions within the additive-subtractive process chain. This includes both the macroscopic geometric scale and the microscopic scale of the material structure. Finally, conclusions and future perspectives are derived and discussed.