In this work the non-equilibrium dilepton production from a hadronic transport approach (SMASH) is presented. The dilepton emission from the hadronic stage is of interest for current HADES results measured at GSI in the beam energy range from 1.25 - 3.5 GeV. Also at high collision energies (RHIC/LHC) the later dilute stages of the reaction are dominated by hadronic dynamics. The newly developed hadronic transport approach called SMASH (=Simulating Many Accelerated Strongly-interacting Hadrons) is introduced first. After explaining the basic interaction mechanisms, a comparison of elementary cross sections for pion production to experimental data is shown. The dilepton production within SMASH is explained in detail. The main contribution to the dilepton spectra in the low energy regime of GSI/FAIR/RHIC-BES originates from resonance decays. Results of the dilepton production with SMASH such as invariant mass spectra are shown.