We investigate ion currents in DNA translocation experiments by means of continuum modelling, coarse grained hybrid Molecular Dynamics/Lattice Boltzmann simulations and, atomistic simulations. The ion current is the key observable in these experiments, where single DNA molecules are dragged through nanometer‐sized pores in membranes, that might even allow to construct DNA sequencing devices based on nanopores. The current modulation caused by the DNA can be decomposed into three physical effects: the exclusion of ions from the DNAs volume; the attraction of counterions; and friction between DNA and ions. We compare the quantitative influence of all three contributions, using models of different resolution, finding, finally, that atomistic simulations provide good agreement with experiments.