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Based on first-principles calculations, we demonstrate the impact of the electric polarization on electron transport in ferroelectric tunnel junctions (FTJs). Using a Pt/BaTiO3 /Pt FTJ as a model system, we show that the polarization of the BaTiO3 barrier leads to a substantial drop in the tunneling conductance due to changes in the electronic structure driven by ferroelectric displacements. We find a sizable change in the transmission probability across the Pt/BaTiO3 interface with polarization reversal, a signature of the electroresistance effect. These results reveal exciting prospects that FTJs offer as resistive switches in nanoscale electronic devices.