  We update theoretical studies of the physics opportunities presented by
mu+mu- Higgs factories. Interesting measurements of the Standard Model Higgs
decays into {\bar b}b, tau+tau- and WW* may be possible if the Higgs mass is
less than about 160 GeV, as preferred by the precision electroweak data, the
mass range being extended by varying appropriately the beam energy resolution.
A suitable value of the beam energy resolution would also enable the
uncertainty in the b-quark mass to be minimized, facilitating measurements of
parameters in the MSSM at such a first mu+mu- Higgs factory. These measurements
would be sensitive to radiative corrections to the Higgs-fermion-antifermion
decay vertices, which may violate CP. Radiative corrections in the MSSM may
also induce CP violation in Higgs-mass mixing, which can be probed via various
asymmetries measurable using polarized mu+mu- beams. In addition,
Higgs-chargino couplings may be probed at a second mu+mu- Higgs factory.
