  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.
