Binary systems with a neutron-star primary accreting from a companion star display variability in the X-ray band on time scales ranging from years to milliseconds. With frequencies of up to ~1300 Hz, the kilohertz quasi-periodic oscillations (kHz QPOs) represent the fastest variability observed from any astronomical object. The sub-millisecond time scale of this variability implies that the kHz QPOs are produced in the accretion flow very close to the surface of the neutron star, providing a unique view of the dynamics of matter under the influence of some of the strongest gravitational fields in the Universe. This offers the possibility to probe some of the most extreme predictions of General Relativity, such as dragging of inertial frames and periastron precession at rates that are sixteen orders of magnitude faster than those observed in the solar system and, ultimately, the existence of a minimum distance at which a stable orbit around a compact object is possible. Here we review the last twenty years of research on kHz QPOs, and we discuss the prospects for future developments in this field.
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