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Phase field simulations suitable to describe interfacial phenomena at the mesoscale require as input parameters accurate interfacial energies as well as the interface mobilities. However, this information is not directly accessible by experiment. Furthermore, phenomena such as impurity segregation cannot be decoupled and their independent role in interfacial cohesion and mobility cannot be deduced. On the other hand ab-initio calculations and/or classical interatomic potentials are suitable tools which can provide an on-atomic-scale description of the interfaces. However, there are a number of challenges that one encounters: multidimensional phase space of the interfacial misorientation degrees of freedom, suitable driving forces, and large length and time scales just to mention a few. In the present report we provide an extended review on the atomistic calculations and the simulation strategies proposed to tackle the corresponding problems.