The physics and world-wide accelerator context for possible accelerator
projects at CERN after the LHC are reviewed, including the expectation that an
e+ e- linear collider in the TeV energy range will be built elsewhere. Emphasis
is laid on the Higgs boson, supersymmetry and neutrino oscillations as
benchmarks for physics after the LHC. The default option for CERN's next major
project may be the CLIC multi-TeV e+ e- collider project. Also interesting is
the option of a three-step scenario for muon storage rings, starting with a
neutrino factory, continuing with one or more Higgs factories, and culminating
in a mu+ mu- collider at the high-energy frontier.Comment: 23 pages LaTeX, 16 figures, to appear in the Proceedings of the
Workshop on the Development of Future Linear Electron-Positron Colliders for
Particle Physics Studies and for Research using Free-Electron Lasers, Lund,
23 - 26 September 1999, misprints concerning Fig. 8 correcte
