This paper 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 for precise measurements of the Higgs boson properties and of the EWSB parameters is presented. Possible follow-on projects, which include an increase of the TLEP centre-of-mass energy to 500~GeV, and complementing TLEP with a 100~TeV pp collider, the VHE-LHC, are described briefly in Section~\ref{sec:VHE-LHC}. Comparisons with the potential of the HL-LHC and of linear collider projects (ILC, CLIC) are made throughout. This paper represents the current, preliminary understanding of the physics potential of TLEP, complemented with mentions of the VHE-LHC reach whenever appropriate. A five-year-long design study -- responding to the recent European Strategy update and part of the CERN medium-term plan~\cite{cite:MTP} for 2014--2018 -- has been launched to refine this understanding, as well as to ascertain the feasibility of TLEP and the VHE-LHC, as input to the next European Strategy update. 