  The spin frequency distribution of accreting millisecond X-ray pulsars cuts
off sharply above 730 Hz, well below the breakup spin rate for most neutron
star equations of state. I review several different ideas for explaining this
cutoff. There is currently considerable interest in the idea that gravitational
radiation from rapidly rotating pulsars might act to limit spin up by
accretion, possibly allowing eventual direct detection with gravitational wave
interferometers. I describe how long-term X-ray timing of fast accreting
millisecond pulsars like the 599 Hz source IGR J00291+5934 can test the
gravitational wave model for the spin frequency limit.
