Energy Frontier DIS at CERN: the LHeC and the FCC-eh

The Large Hadron-electron Collider (LHeC) at CERN is a design study in the context of the LHC luminosity upgrade project, HL-LHC, to establish electron-proton/nucleus collisions with centre-of-mass energies in the TeV regime and luminosities in the order of 10^34𝑐𝑚−2𝑠−1. It implies the construction of an energy recovery linac in racetrack configuration to provide an intense 50 GeV electron beam that will collide with the HL-LHC hadron beams. Such an energy recovery racetrack could also be used at the Future Circular Collider, the FCC-eh, with even higher centre-of-mass energies and similar luminosities. In this paper we will review the status of the project with focus on the accelerator design progress, based on the updated thorough LHeC design report, published in March 2020.