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Selective laser melting (SLM) is one of the most popular additive-manufacturing techniques that are revolutionising the production process by opening up new possibilities for unique product-shape fabrication, generating objects of complex geometry and reducing energy consumption as well as waste. However, the more widespread use of this technology is hindered by a major drawback—the thermal-history-dependent microstructure that is typical of SLM-fabricated objects is linked to uncertainties regarding the crucial material properties. While trial-and-error approaches are often employed to limit these risks, the rapidly developing field of numerical modelling represents a cheap and reliable methodology for predicting the microstructure—and by extension, the mechanical properties—of SLM-fabricated objects. Numerical approaches hitherto applied to predicting the evolution of the microstructure in SLM processes and similar boundary-value problems are reviewed and analysed in this article. The conducted analysis focused on mesoscopic scale models, which currently offer sufficient resolution to recover the key microstructural properties at a computational cost that is low enough for the methodology to be applied to industrial problems.