Computer memory that is non-volatile and therefore able to retain its information even when switched off enables computers that do not need to be booted up. One of the technologies for such applications is ferroelectric random access memories, where information is stored as ferroelectric polarization. To miniaturize such devices to the size of a few nanometres, ferroelectric tunnel junctions have seen considerable interest. There, the electric polarization determines the electrical resistance of these thin films, switching the current on and off. With control over other parameters such as magnetism also being possible, ferroelectric tunnel junctions represent a promising and flexible device design. F erroelectric random access memories (FeRAMs), in which information is encoded through the ferroelectric polarization, are commercially available products with fast write speed, large read/write cycle endurance and low-power consumption 1 . In these ferroelectric capacitors, a ferroelectric thin film (typically 100 nm thick) is sandwiched between two electrodes and the remnant polarization is switched by applying an electric field between the electrodes. The widespread development of these memories is however limited owing to the capacitive readout of the information (the polarization) that prevents the scalability of FeRAMs up to gigabit densities and necessitates the rewriting of information after readout (destructive readout) 2 . In ferroelectric diodes, the current across a thick ferroelectric can be modulated by the polarization at the ferroelectric/electrode interface, giving rise to a non-destructive, resistive readout of the information 3,4 . But in these devices, the large thickness of the ferroelectric layer results in very low readout currents, limiting their miniaturization. As the ferroelectric layer thickness is decreased to a few nanometres, electronic conduction is greatly enhanced as quantum-mechanical tunnelling through the ferroelectric becomes possible 5,6 . These devices in which two electrodes sandwich a ferroelectric tunnel barrier are called ferroelectric tunnel junctions (FTJs). The tunnel transmission may be strongly modulated by the ferroelectric polarization producing giant tunnel electroresistance (TER) with OFF/ON resistance ratios reaching 10 4 (refs 7,8). Moreover, the readout current densities are much larger than in ferroelectric diodes, thereby opening the path to possible applications as high-density ferroelectric memories with non-destructive readout.Here we review the fast progress of the nascent field of FTJs and give perspectives for new physical effects and future applications. We first summarize possible electron transport mechanisms that occur when voltage is applied across ultrathin films of ferroelectrics. We then focus on experimental reports that evidence a direct correlation between ferroelectric switching and resistive switching, from local probes experiments on ferroelectric surfaces to solid-state