Ferroic-order parameters are useful as state variables in non-volatile information storage media because they show a hysteretic dependence on their electric or magnetic field. Coupling ferroics with quantum-mechanical tunnelling allows a simple and fast readout of the stored information through the influence of ferroic orders on the tunnel current. For example, data in magnetic random-access memories are stored in the relative alignment of two ferromagnetic electrodes separated by a non-magnetic tunnel barrier, and data readout is accomplished by a tunnel current measurement. However, such devices based on tunnel magnetoresistance typically exhibit OFF/ON ratios of less than 4, and require high powers for write operations (>1 × 10(6) A cm(-2)). Here, we report non-volatile memories with OFF/ON ratios as high as 100 and write powers as low as ∼1 × 10(4) A cm(-2) at room temperature by storing data in the electric polarization direction of a ferroelectric tunnel barrier. The junctions show large, stable, reproducible and reliable tunnel electroresistance, with resistance switching occurring at the coercive voltage of ferroelectric switching. These ferroelectric devices emerge as an alternative to other resistive memories, and have the advantage of not being based on voltage-induced migration of matter at the nanoscale, but on a purely electronic mechanism.