  In early 1996 a series of discoveries begun with NASA's Rossi X-ray Timing
Explorer of a new, up to then unknown astrophysical phenomenon. It turned out
that accreting low magnetic-field neutron stars show quasi-periodic
oscillations in their X-ray flux at rates of up to more than a kilohertz. These
kHz QPO, now reported from eleven different systems, are among the fastest
phenomena in the sky and can provide us with new information about the
fundamental properties of neutron stars and help testing general relativity in
the strong-field regime. If, for example, their frequencies can be identified
with the Keplerian frequencies of matter in orbit around a 1.4 Solar-mass
neutron star, then the radius of the star would have to be less than 15 km,
which directly constrains the equation of state of bulk nuclear-density matter,
and for an only slightly tighter orbit or slightly more massive neutron star
the orbital radius would equal the Schwarzschild-geometry general-relativistic
marginally stable orbit (12.5 km for a 1.4 Solar mass object). So far all
models that have been put forward for explaining the new phenomenon have
encountered problems. In this paper I review the relatively simple and highly
suggestive phenomenology as it has emerged from the data up to now, and discuss
some of the proposed models.
