  Anapole moments are parity-odd, time-reversal-even moments of the E1
projection of the electromagnetic current. Although it was recognized, soon
after the discovery of parity violation in the weak interaction, that
elementary particles and composite systems like nuclei must have anapole
moments, it proved difficult to isolate this weak radiative correction. The
first successful measurement, an extraction of the nuclear anapole moment of
133Cs from the hyperfine dependence of the atomic parity violation, was
obtained only recently. An important anapole moment bound in Tl also exists. We
discuss these measurements and their significance as tests of the hadronic weak
interaction, focusing on the mechanisms that operate within the nucleus to
generate the anapole moment. The atomic results place new constraints on weak
meson-nucleon couplings, ones we compare to existing bounds from a variety of
p-p and nuclear tests of parity nonconservation.
