The first millisecond X-ray variability phenomena from accreting compact ob
jects have recently been discovered with the Rossi X-ray Timing Explorer Th
ree new phenomena are observed from low-mass X-ray binaries containing low-
magnetic-field neutron stars: millisecond pulsations, burst oscillations, a
nd kilohertz quasi-periodic oscillations. Models for these new phenomena in
volve the neutron star spin and orbital motion close around the neutron sta
r, and rely explicitly on our understanding of strong gravity and dense mat
ter. I review the observations of these new neutron-star phenomena and some
possibly related phenomena in black-hole candidates, and describe the atte
mpts to use these observations to perform measurements of fundamental physi
cal interest in these systems.