Physics with muon colliders

Facilities using intense muon beams would provide an extremely rich physics program for many years. In particular, compact muon co!liders with a centre-of-mass energy from 100 GeV to lOTeV could be a natural extension of a neutrino factory based on this kind of beams. Future options after the Tevatron (Fermilab) or the LHC (CERN) therefore include muon colliders as an interesting possibility. Some of the original aspects of such a program, both from the machine point of view (fast muon cooling, backgrounds, neutrino radiation, ... ) and for its physics· capabilities (large coupling to Higgs bosons, outstanding energy determination, precision tests of the MSSM, ... ) are discussed in some details.