  We summarize the observations of the spin periods of rapidly accreting
neutron stars. If gravitational radiation is responsible for balancing the
accretion torque at the observed spin frequencies of ~300 Hz, then the
brightest of these systems make excellent gravitational wave sources for
LIGO-II and beyond. We review the recent theoretical progress on two mechanisms
for gravitational wave emission: mass quadrupole radiation from deformed
neutron star crusts and current quadrupole radiation from r-mode pulsations in
neutron star cores.
