This paper presents an overview of recent computer simulations of grain boundary (GB)diffusion focusing on atomistic understanding of diffusion mechanisms. At low temperatures when GBstructure is ordered, diffusion is mediated by point defects inducing collective jumps of several atomsforming a chain. At high temperatures when GB structure becomes highly disordered, the diffusionprocess can be analyzed by statistical methods developed earlier for supercooled liquids and glasses.Previous atomistic simulations reported in the literature as well as the new simulations presented in thispaper reveal a close similarity between diffusion mechanisms in GBs and in supercooled liquids. GBdiffusion at high temperatures is dominated by collective displacements of atomic groups (clusters),many of which have one-dimensional geometries similar to strings. The recent progress in this fieldmotivates future extensions of atomistic simulations to diffusion in alloy GBs, particularly in glassformingsystems.