  We discuss the capabilities of future muon colliders to resolve important
particle physics questions. A collider with c.m. energy $\sqrt s = 100$ to
500~GeV offers the unique opportunity to produce Higgs bosons in the
$s$-channel and thereby measure the Higgs masses, total widths and several
partial widths to high precision. At this same machine, $t\bar t$ and $W^+W^-$
threshold studies would yield superior precision in the determination of $m_t$
and $m_W$. A multi-TeV $\mu^+\mu^-$ collider would open up the realm of physics
above the 1 TeV scale, allowing, for example, copious production of
supersymmetric particles up to the highest anticipated masses or a detailed
study of the strongly-interacting scenario of electroweak symmetry breaking.
