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This thesis contributes to the field of soft matter research and studies the importance of hydrodynamic interactions during free-solution electrophoresis of linear polyelectrolytes by means of coarse-grained molecular dynamics simulations including full electro-hydrodynamic interactions. The center of attention is the specific role of hydrodynamic interactions on the electrophoretic behaviour of charged macromolecules. Points of interest are the dependence of hydrodynamic interactions on the chain length, the chain flexibility and the surrounding counterions, and their combined influence on important observables such as the static chain conformations and the dynamic transport coefficients, i.e., the diffusion and the electrophoretic mobility. These problems are addressed by extensive computer simulations that are quantitatively matched with experimental results. Existing theoretical predictions are carefully examined and are augmented by the observations in this thesis.