Additive manufacturing is a technology rapidly expanding on a number of industrial sectors. It provides design freedom and environmental/ecological advantages. It transforms essentially design files to fully functional products. However, it is still hampered by low productivity, poor quality and uncertainty of final part mechanical properties. The root cause of undesired effects lies in the control aspects of the process. Optimization is difficult due to limited modelling approaches. Physical phenomena associated with additive manufacturing processes are complex, including melting/ solidification and vaporization, heat and mass transfer etc. The goal of the current study is to map available additive manufacturing methods based on their process mechanisms, review modelling approaches based on modelling methods and identify research gaps. Later sections of the study review implications for closed-loop control of the process.