The prospects for a muon collider operated as a Higgs factory are reviewed. The large muon mass means that the s-channel Higgs production mechanism is available, and simultaneously suppresses bremsstrahlung so that the beam energy spread can be kept to the MeV level required to exploit this. Thus this is the only machine which can make a direct scan over the Higgs resonance, and make an extraordinary mass measurement. Further possibilities such as a scan of the H and A of supersymmetry and CP violation are also mentioned.
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