The dramatic discovery with the Rossi X-Ray Timing Explorer satellite
of remarkably coherent similar to 300-1200 Hz oscillations in the X-ra
y brightness of some sixteen neutron stars in low-mass binary systems
has spurred theoretical modeling of these oscillations and investigati
on of their implications for the neutron stars and accretion flows in
these systems. High-frequency oscillations are observed both during th
ermonuclear X-ray bursts and during intervals of accretion-powered emi
ssion and appear to be a characteristic feature of disk-accreting neut
ron stars with weak magnetic fields. In this review we focus on the hi
gh-frequency quasi-periodic oscillations (QPOs) seen in the accretion-
powered emission. We first summarize the key properties of these kiloh
ertz QPOs and then describe briefly the models that have been proposed
to explain them. The existing evidence strongly favors beat-frequency
models. We mention several of the difficulties encountered in applyin
g the magnetospheric beat-frequency model to the kilohertz QPOs. The m
ost fully developed and successful model is the sonic-point beat-frequ
ency model. We describe the work on this model in some detail. We then
discuss observations that could help to distinguish between models. W
e conclude by noting some of the ways in which study of the kilohertz
QPOs may advance our understanding of dense matter and strong gravitat
ional fields.