Muon colliders offer special opportunities to discover and study new physics. With the high intensity source of muons at the front end, orders of magnitude improvements would be realized in searches for rare muon processes, in deep inelastic muon and neutrino scattering experiments, and in long-baseline neutrino oscillation experiments. At a 100 to 500 GeV muon collider, neutral Higgs boson (or techni-particle) masses, widths and couplings could be precisely measured via s-channel production. Also, threshold cross-section studies of W+ W-, t t-bar, Zh and supersymmetric particle pairs would precisely determine the corrresponding masses and test supersymmetric radiative corrections. At the high energy frontier a 3 to 4 TeV muon collider is ideally suited for the study of scalar supersymmetric particles and extra Z-bosons or strong WW scattering.

Latex2.09 using aipproc.sty (included) and epsf.sty. 15 pages, 11 postscript figures. Invited talk at the 4th International Conference on the Physics Potential and Development of mu+ mu- Colliders, San Francisco, December 1997