Additive manufacturing (AM) is a very promising technology; however, there are a number of open issues related to the different AM processes. The literature on modelling the existing AM processes is reviewed and classified. A categorization of the different AM processes in process groups, according to the process mechanism, has been conducted and the most important issues are stated. Suggestions are made as to which approach is more appropriate according to the key performance indicator desired to be modelled and a discussion is included as to the way that future modelling work can better contribute to improving today's AM process understanding