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The cost, size and availability of electron accelerators are dominated by the achievable accelerating gradient. Conventional high-brightness radio-frequency accelerating structures operate with 30–50 MeV m⁻¹ gradients. Electron accelerators driven with optical or infrared sources have demonstrated accelerating gradients orders of magnitude above that achievable with conventional radio-frequency structures. However, laser-driven wakefield accelerators require intense femtosecond sources and direct laser-driven accelerators suffer from low bunch charge, sub-micron tolerances and sub-femtosecond timing requirements due to the short wavelength of operation. Here we demonstrate linear acceleration of electrons with keV energy gain using optically generated terahertz pulses. Terahertz-driven accelerating structures enable high-gradient electron/proton accelerators with simple accelerating structures, high …