In the first talk, we will present tentative design parameters, novel concepts and accelerator-physics challenges for these two circular e+e− Higgs-factory colliders. They both require – in addition to the collider ring – a fast cycling accelerator ring for quasi-continuous top-up injection to compensate for the short beam lifetime due to radiative Bhabha scattering. In addition, a large momentum aperture and flat beams are needed to ensure an adequate beam lifetime with regard to beamstrahlung. Both TLEP and LEP3 become Tera-Z factories when operated around the Z pole. The 80-km tunnel of TLEP would also provide a path towards much higher energies, e.g. it could later accommodate a very high energy LHC (“VHE-LHC”), with a centre-of-mass energy approaching 100 TeV in pp collisions.
