This article provides a literature review of finite element simulation studies for metallic powder bed additive manufacturing processes. The various approaches in the numerical modeling of the processes and the selection of materials properties are presented in detail. Simulation results are categorized according to three major findings’ groups (i.e. temperature field, residual stresses and melt pool characteristics). Moreover, the means used for the experimental validation of the simulation findings are described. Looking deeper into the studies reviewed, a number of future directions are identified in the context of transforming simulation into a powerful tool for the industrial application of additive manufacturing. Smart modeling approaches should be developed, materials and their properties should be further characterized and standardized, commercial packages specialized in additive manufacturing simulation have to be developed and simulation needs to become part of the modern digital production chains. Finally, the reviewed studies are organized in a table and characterized according to the process and material studied, the modeling methodology and the experimental validation method used in each of them. The key findings of the reviewed studies are also summarized.