Stellar-mass black holes observed in X-rays are spun up by accretion from a companion and many seem to spin close to or at the physically allowed limit imposed by the Kerr metric. The same does appear to be true for neutron stars, with a maximum reported spin of 716 Hz for PSR J1748-2446ad, which is less than half of the estimated breakup rotational frequency for a typical neutron star. R-modes (also called Rossby waves) have been proposed as a possible mechanism for limiting the spins of accreting neutron stars. The r-mode instability mechanism can also potentially make a rotating neutron star into a strong source of gravitational waves, but the shape of the instability window depends on details of the neutron star equation of state and viscosity. I will briefly review the theory of CFS instabilities and discuss some tantalizing hints of r-modes, possibly observed as modulations in the emission of millisecond pulsar XTE J1751-305 and 4U 1636-536, some puzzles (such as LMXBs which seem to sit in the middle of the instability window) and current upper limits on continuous gravitational wave detections by LIGO.