The two-loop electroweak radiative corrections to the muon's
anomalous magnetic moment, $a_\mu\equiv (g_\mu-2)/2$, are presented.
We obtain an overall 22.6\%
reduction in the
electroweak contribution $a_\mu^{\rm EW}$ from $195\times 10^{-11}$ to
$151(4)\times 10^{-11}$. Implications for the full standard model
prediction and
an upcoming high precision measurement of $a_\mu$ are briefly discussed.
Some aspects of the calculations are discussed in detail.