  The dramatic discovery with the Rossi X-Ray Timing Explorer satellite of
remarkably coherent $\sim$300--1200 Hz oscillations in the X-ray brightness of
some sixteen neutron stars in low-mass binary systems has spurred theoretical
modeling of these oscillations and investigation of their implications for the
neutron stars and accretion flows in these systems. High-frequency oscillations
are observed both during thermonuclear X-ray bursts and during intervals of
accretion-powered emission and appear to be a characteristic feature of
disk-accreting neutron stars with weak magnetic fields. In this review we focus
on the high-frequency quasi-periodic oscillations (QPOs) seen in the
accretion-powered emission. We first summarize the key properties of these
kilohertz 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 applying the magnetospheric
beat-frequency model to the kilohertz QPOs. The most fully developed and
successful model is the sonic-point beat-frequency model. We describe the work
on this model in some detail. We then discuss observations that could help to
distinguish between models. We conclude by noting some of the ways in which
study of the kilohertz QPOs may advance our understanding of dense matter and
strong gravitational fields.
