Despite considerable evidence verifying that millisecond pulsars are spun up through sustained accretion in low-mass X-ray binaries (LMXBs), it has proven surprisingly difficult to actually detect millisecond X-ray pulsars in LMXBs. There are only 5 accretion-powered millisecond X-ray pulsars known among more than 80 LMXBs containing neutron stars, but there are another 11 nuclear powered millisecond pulsars which reveal their spin only during brief, thermonuclear X-ray bursts. In addition, 2 of the accretion-powered pulsars also exhibit X-ray burst oscillations, and their unusual properties, along with the absence of persistent pulsations in most LMXBs, suggest that the magnetic fields in many LMXBs may be hidden by accreted material. Interestingly, the nuclear-powered pulsars offer a statistically unbiased probe of the spin distribution of recycled pulsars and show that this distribution cuts off sharply above 730 Hz, well below the breakup spin rate for most neutron star equations of state. This indicates that some mechanism acts to halt or balance spin-up due to accretion and that submillisecond pulsars must be very rare (and are possibly nonexistent). It is unclear what provides the necessary angular momentum sink, although gravitational radiation is an attractive possibility.
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