  The first millisecond X-ray variability phenomena from accreting compact
objects have recently been discovered with the Rossi X-ray Timing Explorer.
Three new phenomena are observed from low-mass X-ray binaries containing
low-magnetic-field neutron stars: millisecond pulsations, burst oscillations
and kiloHertz quasi-periodic oscillations. Models for these new phenomena
involve the neutron star spin, and orbital motion closely around the neutron
star and rely explicitly on our understanding of strong gravity and dense
matter. I review the observations of these new neutron-star phenomena and
possibly related ones in black-hole candidates, and describe the attempts to
use them to perform measurements of fundamental physical interest in these
systems.
