Abstract
The remarkable discovery of kilohertz quasi-periodic brightness oscillations (QPOs) in the accretion-powered emission from some sixteen neutron-star low-mass X-ray binary systems has led to much speculation about and theoretical modeling of the origin of these oscillations. It has also led to intense study of the implications that these QPOs have for the properties of neutron stars and of the accretion flow onto them. In this review we describe the strengths and weaknesses of the models that have been proposed for the kilohertz QPOs observed in the accretion-powered emission. We conclude that beat-frequency models, and in particular the sonic-point model, are currently the most promising. If these models are correct, the kilohertz QPOs provide the strongest constraints to date on the masses and radii of neutron stars in low-mass X-ray binaries, and on the equation of state of the dense matter in all neutron stars.
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