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\section{Introduction}  \label{sec:intro}  The Higgs boson with mass around 125 GeV recently discovered by the ATLAS and CMS experiments~\cite{v_Aben_Abi_Abolins_et_al__2012,gicevic_Ero_Fabjan_et_al__2012} at the CERN-LHC LHC  is found to have properties compatible with the Standard Model predictions~\cite{ATLASHiggsCouplings,Ero_Fabjan_Friedl_et_al__2013}, as shown for example in Fig.~\ref{fig:ellis}~\cite{cite:1303.3879}. Coupled with the absence of any other indication so far for new physics at the LHC, be it either through precision measurements or via direct searches, this fundamental observation seems to push the energy scale of any physics beyond the Standard Model above several hundred GeV. The higher-energy LHC run, which is expected to start in 2015 at $\sqrt{s} \sim 13$-$14$ TeV, will extend the sensitivity to new physics to 1 TeV or more. Fundamental discoveries may therefore be made in this energy range by 2017-2018. Independently of the outcome of this higher-energy run, however, there must be new phenomena, albeit at unknown energy scales, as shown by the evidence for non-baryonic dark matter, the cosmological baryon-antibaryon asymmetry and non-zero neutrino masses, which are all evidence for physics beyond the Standard Model. In addition to the high-luminosity upgrade of the LHC, new particle accelerators will be instrumental to understand the physics underlying these observations.