New types of particle accelerators that could achieve multi Giga-electron volts per metre (GeV/m) accelerating gradients are of utmost importance to reduce the size and cost of future generations of high energy colliders as well as provide a widespread availability of compact accelerator technology to smaller laboratories around the world. Gradients in the order of 100 MeV/m have been achieved by conventional techniques and are limited by RF-induced plasma breakdown. Beam driven dielectric wakefield accelerators (DWAs) typically operate in the Terahertz frequency range, which pushes the plasma breakdown threshold for surface electric fields into the multi-GV/m range. DWA technique allows to accommodate a significant amount of charge per bunch, and gives an access to conventional fabrication techniques for the accelerating structures. To date 0.3 GeV/m accelerating and 1.3 GeV/m decelerating gradients have been achieved using a dielectric lined waveguide with sub-millimetre transverse aperture.