Anisotropy in grain boundary "thermo-kinetics" is central to our understanding of microstructural evolution during grain growth and recrystallization. This paper focusses on role of atomic-scale computer simulation techniques, in particular molecular dynamics (MD), in extracting fundamental grain boundary properties and elucidating the atomic-scale mechanisms that determine these properties. A brief overview of recent strides made in extraction of grain boundary mobility and energy is presented, with emphasis on plastic strain induced boundary motion (p-SIBM) during recrystallization and curvature driven boundary motion (CDBM) during grain growth. Simulations aimed at misorientation dependence of the grain boundary properties during p-SIBM and CDBM show that boundary mobility and energy exhibit extrema at high symmetry misorientations and boundary mobility is comparatively more anisotropic during CDBM. This suggests that boundary mobility is dependent on the driving force. Qualitative observations of the atomic-scale mechanisms in play during boundary motion corroborate the simulation data. p-SIBM is dominated by motion of dislocation-interaction induced stepped structure of the grain boundaries, while correlated shuffling of group of atoms preceded by rearrangement of grain boundary free volume due to single atomic-hops across the grain boundary is frequently observed during CDBM. Comparison of the simulation results with high-purity experimental data extracted in Al indicates that while there is excellent agreement in misorientation dependent anisotropic properties, there are significant differences in values of boundary mobility and migration activation enthalpy. This strongly suggests that minute concentration of impurities retard grain boundary kinetics via impurity drag. Finally, the paper briefly discusses current and future challenges facing the computer simulation community in studying grain boundary systems in real materials where extrinsic effects (vacancy, impurity, segregation and particle effects) significantly alter the microscopic structure-mechanism relations and play a decisive role in determining the boundary properties.