During the last years, direct digital manufacturing of metallic components directly from electronic data based on layer-by-layer fabrication has developed from rapid prototyping to additive manufacturing (AM). For the first time, the design of components is no longer strongly restricted by the production method, i.e. individual parts with a high complexity can be realized without taking into account specific design rules, e.g. cellular structures, complex internal structure or cooling channels. This offers many advantages: complex geometry, weight reduction, short lead time, integration of functions, etc. However, the layer-by-layer processing combined with directional and rapid solidification also offers the possibility to design the local microstructure of the resulting component. Based on numerical simulation sophisticated processing strategies allow to prevent binding faults, to tailor the grain structure or phase composition of high performance alloys such as nickel-base superalloys or titanium aluminides. In this contribution, a short introduction into powder bed fusion based additive manufacturing is given. The fundamental physical phenomena are reviewed, which have to be considered, in order to describe microstructure evolution during AM. Physical models and numerical approaches for different problems are presented and critically discussed. Selected numerical examples representing different building scenarios demonstrate the predictive power of numerical tools. Special emphasis is put on the stochastic effect of the powder, the development of optimized processing strategies, the evolution of the grain structure and the possibility to tailor the phase composition through targeted selective evaporation.