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In many simulations in computational science and engineering a partial differential equation has to be solved. Multigrid methods are among the fastest methods for accomplishing this task, in many cases with optimal, i.e., O(N), complexity. As a consequence, in simulations of huge problems on large-scale supercomputers often a multigrid method is used. If the underlying problem is formulated on a structured grid, this structure can be exploited in the multigrid method to build up the grid hierarchyd. Additionally, the presence of structure allows for a relatively straightforward efficient implementation on modern computer architectures, like modern CPUs or GPUs. Further, structure allows for a rigorous analysis of the problem and the multigrid method used for solving it. Still, the used multigrid components, i.e., grid transfer operators and smoothers, have to be carefully chosen to be able to treat the underlying problem. Besides the adaption to the problem the chosen component can have a huge influence on the serial efficiency and the parallel scalability of the whole method. In this talk multigrid methods for structured grids, their analysis and the specific choice of algorithmic components for parallel computers will be discussed.