The development speed and application range of the additive manufacturing (AM) processes, such as selective laser melting (SLM), laser metal deposition (LMD) or laser-engineering net shaping (LENS), are ever-increasing in modern advanced manufacturing field for rapid manufacturing, tooling repair or surface enhancement of the critical metal components. LMD is based on a kind of directed energy deposition (DED) technology which ejects a strand of metal powders into a moving molten pool caused by energy-intensive laser to finally generate the solid tracks on the workpiece surface. Accurate numerical modelling of LMD process is considered to be a big challenge due to the involvement of multiple phase changes and accompanied mass and heat flows. This paper overviews the existing advancement of additive manufacturing, especially its subcategory relating to the DED. The LMD process is analyzed in detail and subsequently broken down to facilitate the simulation of each physical stage involved in the whole process, including powder transportation and dynamics, micro-mechanical modelling, formation of deposited track and residual stress on the substrate. The proposed modelling considerations and a specific CFD model of powder feeding will assist in accurately simulating the DED process; it is particularly useful in the field of aerospace manufacturing which normally has demanding requirements on its products.