In recent years, studies have demonstrated that grain boundary (GB) migration is a three-dimensional (3D) process, characterized by a 3D mobility tensor. In this presentation, we introduce a recently developed 3D interface random walk theory, which provides a framework for extracting intrinsic GB mobility and shear coupling tensors based on the random walk behavior of GB positions. This theory enables a mathematical proof of the symmetry of the GB mobility tensor in the case of overdamped GB migration. The theory and its conclusions align with molecular dynamics simulation results, and the computed shear coupling aligns closely with predictions from disconnection analysis. Additionally, we propose the fast-adapted random walk (FAIRWalk) method, enabling the efficient extraction of the GB mobility tensor from fewer simulations while maintaining high accuracy. Building on this advancement, we conducted an extensive survey of the mobility, shear coupling, and activation energy of the migration of 388 coincidence-site lattice Ni GBs in the Olmsted database. Several intriguing phenomena were observed, including temperature-induced sudden emergence, disappearance, or inversion of shear coupling; GBs with "zero" normal mobility but high shear mobility; and a non-linear relationship between activation energy and mobility. These findings challenge the traditional understanding of GB migration and warrant further investigation.