  A review of the experimental and theoretical determinations of the anomalous
magnetic moment of the muon is given. The anomaly is defined by a=(g-2)/2,
where the Land\'e g-factor is the proportionality constant that relates the
spin to the magnetic moment. For the muon, as well as for the electron and
tauon, the anomaly a differs slightly from zero (of order 10^{-3}) because of
radiative corrections. In the Standard Model, contributions to the anomaly come
from virtual `loops' containing photons and the known massive particles. The
relative contribution from heavy particles scales as the square of the lepton
mass over the heavy mass, leading to small differences in the anomaly for e,
\mu, and \tau. If there are heavy new particles outside the Standard Model
which couple to photons and/or leptons, the relative effect on the muon anomaly
will be \sim (m_\mu/ m_e)^2 \approx 43\times 10^3 larger compared with the
electron anomaly. Because both the theoretical and experimental values of the
muon anomaly are determined to high precision, it is an excellent place to
search for the effects of new physics, or to constrain speculative extensions
to the Standard Model. Details of the current theoretical evaluation, and of
the series of experiments that culminates with E821 at the Brookhaven National
Laboratory are given. At present the theoretical and the experimental values
are known with a similar relative precision of 0.5 ppm. There is, however, a
3.4 standard deviation difference between the two, strongly suggesting the need
for continued experimental and theoretical study
