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Among the various proposals of Higgs factories (pp colliders, $\epem$ colliders, $\mu^+\mu^-$ colliders, or $\gamma\gamma$ colliders), it turns out that only circular $\epem$ colliders can deliver the integrated luminosity deemed adequate to reach such precisions. The TLEP proposal~\cite{cite:TLEP}, which would be hosted in a new 80 to 100 km tunnel in the Geneva area, would be able to produce collisions at centre-of-mass energies between $m_{\rm Z}$ and 350-370 GeV at several interaction points, and make precision measurements at the Z pole, at the WW threshold, at the HZ cross section maximum and at the $\ttbar$ threshold with an unprecedented accuracy. This collider is also the only project with a possible upgrade to a hadron collider (called VHE-LHC) in the same tunnel, at a centre-of-mass energy of 100 TeV, which would give access to new physics up to scales of 10 TeV or more.  This note is organized as follows. The main characteristics of the TLEP collider relevant for the physics case are summarized in Section~\ref{sec:exp}. In Sections~\ref{sec:Higgs} and~\ref{sec:EWSB}, an overview of the TLEP potential towards precise measurements of the Higgs boson properties and of EWSB parameters is presented. Finally, a brief account of the potential of VHE-LHC is given in Section~\ref{sec:VHE-LHC}. A comparison with the potential of the HL-LHC and of linear collider projects (ILC, CLIC) is made throughout.