  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.
