We consider partial differential equations in non-smooth three-dimensional domains. A finite element method with optimal convergence requires anisotropic mesh refinement towards edges with large internal angles. Such meshes contain elements with a small mesh size perpendicularly to the edge (in the direction of the rapid variation of the solution) and a much larger mesh size in the direction of the edge. For a motivation we compare anisotropic and isotropic mesh refinement in selected examples and focus on a-priori error estimates. In the second part we suggest a multigrid scheme combining semi-coarsening and line smoothers to obtain a solver of optimal algorithmic complexity for anisotropic meshes along edges. Modern discretization methods do not work on one fixed mesh but adapt it iteratively to the solution. Besides reliable and efficient a-posteriori error estimators, further information like the desired stretching direction and the appropriate aspect ratio of the elements are necessary to obtain for the adaptive refinement. The optimal reconstruction of the mesh is one of the current challenges.