  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.
